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CORRELATION OF SOME PSYCHO-
LOGICAL AND EDUCATIONAL
MEASUREMENTS
WITH SPECIAL ATTENTION TO THE
MEASUREMENT OF MENTAL ABILITY
BY
WILLIAM ANDERSON McCALL, Ph.D.
TEACHERS COLLEGE, COLUMBIA UNIVERSITY
CONTRIBUTIONS TO EDUCATION, No. 79
PUBLISHED BY
EtatlftrB (EoUe^f, CfEoIttmbta Intvrrjettg
NEW YORK CITY
1916
A-
Copyright, 1916, by
William Anderson McCall
ACKNOWLEDGMENTS
Aid in this study is but one of a hundred things for which I
am grateful to Professor E. L. Thorndike. Nor shall I forget
the kindness of Professor H. A. Ruger. I also wish to thank
Misses Genevieve L. Coy and Alma R. Huestis for much help-
ful assistance. It was by the courtesy of the New York State
Commission on Ventilation that I could use the data for this
study.
w. A. M.
CONTENTS
I. Problems
II. Experimental Material and Method . . ■ • 3
1. Subjects.
2. Tests with Their Administration and Scoring.
III. Statistical Treatment of Results lo
1. Raw and Corrected Arrays.
2. Deviations and Their Combination.
3. Calculation of Raw Coefficients of Correlation.
4. Calculation of Corrected Coefficients of Correlation.
5. Reliability Coefficients.
IV. Consideration of Problems and Comparison of Results
WITH Those of Other Experimenters .... 35
What Are the Intercorrelation among Some Recent Edu-
cational and Vocational Measurements and Certain Tra-
ditional Tests?
What Is the Order of Each Test's Correlation with Men-
tal Ability?
How Close Is the Correlation of Each Test with Mental
Ability?
What Is the Practical Significance of These Tests for
Educational and Vocational Diagnosis and Guidance?
What Are Some Theoretical Considerations Growing out
of This Study?
V. Conclusion .67
VI. Bibliography 69
VII. Appendix 71
CORRELATION OF SOME PSYCHOLOGICAL AND
EDUCATIONAL MEASUREMENTS
PROBLEMS
"The results of all good experimental work will live, but as
yet most of them are like hieroglyphics awaiting their decipher-
ing Rosetta Stone." These are the words of Spearman. Such
words are true of all fields of research, but they are worse than
true of the field of Correlational Psychology. The Rosetta Stone
of Correlational Psychology must do more than interpret ; it must
reconcile . For this nothing less than a Philosopher's Stone will
suffice, and Science, succeeding Black Magic, fully realizes that
such a stone will not be found, but must be formed by a slow
and laborious process. It is the hope that this study will con-
tribute its small part to the making.
Correlational Psychology is in this more or less chaotic condi-
tion, not only because of poor experimental technique and diverse
and inadequate statistical methods, but also because of the very
great complexity, importance, and number of the problems which
it has elected to attack. Such complexity, importance, and num-
ber of problems is revealed by a very brief survey of the litera-
ture on correlation. But not to go farther afield, it is excellently
illustrated by the problems which it is the purpose of this re-
search to examine. These problems follow:
1. What are the intercor relations among our psychological and
educational tests or the functions which they measure?
2. What is the relative value of each test as a measure of
mental ability ?
3. In the practical measurement of mental ability for educa-
tional and vocational purposes which tests are the more valuable ?
2 Correlation of Psychological and Educational Measurements
4. In the construction and in the application of psychological
tests for the measurement of mental ability, do 'speed' tests or
'power' tests offer more promise, whether as to correlation, con-
venience, or time spent?
5. What characteristics in a test make for high correlation with
mental ability ?
6. What is the value of improvement as a measure of mental
ability ?
7. What is the significance of chronological age as an intel-
lectual index?
8. Is there such a thing as a negative correlation between de-
sirable traits? Is the law of human nature correlation or
compensation ?
g. Do our results support Spearman's "Theorem of the Uni-
versal Unity of Intellective Function," or Burt's "Hierarchy of
the Specific Intelligences"?
These problems have been attacked experimentally. The fol-
lowing pages describe the experiment, the use made of the data,
and the results obtained. This experiment was devised originally
to study problems other than those considered here. In fact,
this study was not even conceived until the experiment was com-
pleted. While this means a certain roughness of technique, it
has the advantage of guaranteeing the impartiality of the data.
II
EXPERIMENTAL MATERIAL AND METHOD
I. Subjects
The subjects for this experiment were eighty-eight public
school children of an average age of about twelve and one-half
years and about equally divided as to sex. These eighty-eight
children were two typical 6B classes in a typical elementary school
in New York City. The two class rooms adjoined and the teach-
ers who had charge of the children used the departmental method
of instruction. That is, the two teachers divided the subjects to
be taught equally between them and each taught her allotted sub-
jects to both classes. In this way both classes received exactly
the same instruction. The classes were equal in mental ability
as measured by what is later described as the six preliminary
tests, though the last fact is not essential to this study. Further,
it should be noted that while children were at the beginning
shifted from one room to the other in order to make the classes
equal in ability, in no case were children specially brought in
from other classes. The eighty-eight children who made up the
two classes were the children the experimenter found there when
he began the experiment — ^they were typical classes.
2. Tests with Their Administration and Scoring
The general plan of the experiment was to give six preliminary
tests, to follow these with an extended practice series, and to con-
clude with six final tests which were to be similar to, but not
identical with, the six preliminary ones. Certain special tests
were given along with the practice series without interrupting it.
In the administration of the tests every effort was made to
treat both classes exactly alike. This was all the easier because
4 Correlation of Psychological and Educational Measurements
a test in one room was followed immediately by the same test in
the other room. Written instructions were used at the beginning
of each new test to avoid unconscious variation. During the
practice series each class was tested for about half an hour. The
testing began in one room half an hour after lunch and was con-
cluded in the other room half an hour before the children were
dismissed. The beginning class on one day would be the conclud-
ing class on the following day. A teacher was always present
when the children were being tested, though she took no part in
the administration of the tests. The entire experiment was con-
ducted by the author with the exception of the six preliminary and
six final tests. Each of these sets was given to both classes in
one day. This required an assistant, but even here the writer
started every test and left the assistant to collect the papers.
This experiment was throughout a group experiment, there
being no individual testing. The detailed method for the practice
series was as follows: The experimenter entered the class room
and announced the names of the three pupils making the highest
scores in each of the tests on the previous day. In addition to
the regular procedure, if a new test were beginning, instructions
were read and what was to be done was illustrated. Otherwise,
the monitors distributed material face down. At the signal:
Hands Up ! all raised their hands. At the signal : Go ! all began
the test. At the signal: Stop! all ceased immediately, wrote
their names and identification numbers on the sheets and turned
them over to the monitors, who did the collecting. This was
repeated for the other tests of that day, after which the experi-
menter went through a similar procedure with the other class.
The tests used on any one day during the practice series, the
number of days they were used, the dates they were used, together
with the average score made by both classes in each test are all
shown in Table A. A brief description of the tests employed,
the time allowed for each, and the method of scoring are given
below.
Preliminary and Final Tests
Visual Vocabulary: The children were given the Thomdike
Reading Scale A, which contains forty-three words. The first
five words are easy and equally difficult. Each succeeding group
Experimental Material and Method 5
of five words grows progressively more difficult. The last group,
consisting of only three words, is the most difficult of all. Thus
both the lower and upper limits of the ability of the children were
measured. The children were to write the letter F under every
word that meant a flower, and the letter A under every word that
meant an animal, and so on. In this as in all the preliminary
and final tests the time allowance was thirty minutes. If a child
completed a test, leaving nothing undone, before the expiration
of the half-hour, he could hand his paper to the experimenter.
This last rule held not only for all the preliminary and final
tests but also for the special tests which were sprinkled along
during the practice experiment. The Visual Vocabulary was
scored in terms of penalties :
Score = Errors -|- Omissions.
The final Visual Vocabulary Test was similar to, though not
identical with, the one just described. The two tests were ad-
ministered and scored in exactly the same way.
Reading: Thorndike's Reading Scale Alpha was used. This
scale contains four paragraphs, each one being more difficult to
comprehend than the preceding. Each paragraph was followed
by several questions. The child's written answers to these ques-
tions were taken as a measure of his comprehension of the para-
graph. A complete sentence was not required of the child, one
word sometimes being sufficient to express the idea. Time al-
lowed : 30 minutes.
Score == 2 (correct answers) -|- i (semi-correct answers).
The final Reading Test is similar. I, J, K and L of Thorndike's
longer Reading Scale were used. The scoring was identical.
Completion: The Trabue Completion Test, consisting of
twenty-eight mutilated sentences, was used. The difficulty of
completing the first sentence is small, but there is a gradual in-
crease in difficulty with each succeeding one. The child was to
write in the missing word or words. Time allowed : 30 minutes.
Score = 2 (sentences completed correctly) -|- ^ (sentences
completed semi-correctly) .
A similar set of twenty-eight sentences was employed in the
same way for the final test.
Arithmetic: Six problems in arithmetic, which grew progres-
sively more difficult, were selected for this test. The child
6 Correlation of Psychological and Educational Measurements
handed in his work with his answers, but only the answers which
were correct received a score.
Score = Number of problems correctly solved.
Six similar problems were used for the final test.
Omnibus I A: The Omnibus Test is so called because it rep-
resents a compilation by Professor Thorndike of several tests
which psychology has found valuable. These are Easy and Hard
Opposites, Verb-Object, Supraordinate, Mixed Relation, Easy
and Hard Direction, and Addition. Time allowed: Thirty min-
utes. The method of scoring this as all the other Omnibus Tests
varied with each special part, hence it would be tedious to give it.
The method used was that devised by Professor Thorndike.
Anyone who desires to use these tests is referred, for a copy
of the method of scoring, to the Department of Educational
Psychology, Teachers College.
The Final Test was Omnibus I B which includes the same
tests as the one just described, the only difference being a slight
variation of the tasks.
Omnibus II A: This tested reasoning ability, the ability to give
the opposites to certain hard words, the ability to give a verb to
a specified subject and to add the proper letters to unfinished
words, and the ability to solve certain problems in arithmetic.
Time allowed : Thirty minutes.
Omnibus II B or the Final Test is a slight variation of Omni-
bus II A.
Special Tests
Proverb: The Proverb Test was recently devised by Professor
H. A. Ruger. It consists of thirteen English proverbs followed
by their corresponding African proverbs. In some the similarity
is easy to perceive; in others it is more difficult. The children
were to match the proverbs. Time allowed : Fifteen minutes.
Score = Number correctly matched.
Other special tests were given from time to time but since these
tests were not given twice they have not been used in this study.
It is necessary that there be two measures of a function if a corre-
lation is to be corrected for attenuation. The Ruger Proverb
Test has been retained just because it was recently devised.
Age: Because of its possible significance, the age of reaching
Experimental Material and Method 7
the grade has been used as a measure of the children. This age
measure was taken from the official school record, and is ex-
pressed in months.
School Mark: This measure was an average of all the marks
given by the two teachers to each child in each subject taught
during the semester in which this experiment was being carried
on. No previous marks have been used.
Teacher Rank: The two teachers were each asked to rank the
eighty-eight children for mental ability. These ratings were
made independently, although it must be remembered that the
teachers had often talked together concerning the children.
Practice Tests
Cancellation of 2's: For this the Woodworth- Wells Cancella-
tion Sheet was used. This sheet contains a series of groups of
five figures arranged in random order. The children were di-
rected to cancel the figure 2. Time allowed: One minute.
Score = 2 (number cancelled correctly) — 2 (number omit-
ted) — 3 (number wrongly marked).
Cancellation of 3's: Exactly the same test as the above, except
that the children cancelled the figure 3.
Cancellation of A's: On the Cancellation A Sheet fifty capital
letter A's were arranged at random among other letters of the
alphabet of which there were fifty each. The children cancelled
the letter A. The time allowed and the scoring were as in the
Cancelling 2 Test.
Cancellation of S's: In every respect the same as the preceding
test except that the letter S was cancelled.
Addition: The Addition sheet employed by Thorndike, Kirby,
and others was used in this test. It is made up of columns of
ten one-place numbers arranged in random order, no figure less
than 2 being used. The children were to write the sum of each
column of figures. Four similar sheets were rotated to prevent
memorizing. Time allowed: Ten minutes.
Score = Number of columns added correctly.
Copying Addresses: This test was recently devised by Profes-
sor Thorndike. A sheet containing twenty-five names arranged
in alphabetical order was given to each child, together with the
small directory from which the names were taken. The children
8 Correlation of Psychological and Educational Measurements
found in the directory the New York City address and wrote it
beside the appropriate name. A different list of names was
used each day. Time allowed: Ten minutes.
Score = Number of addresses correctly copied.
Handwriting: Similar paragraphs were cut from the Youth's
Companion and pasted on cards. Each child was given a para-
graph and a sheet of blank paper with directions to copy as much
of the paragraph as he could while writing as well as he could.
This test was given twice each day, a new paragraph being used
each time. It need hardly be said that in this test as well as
the others all the children did exactly the same thing in any one
test. Time allowed : Four minutes for each test.
Score = I (number of lines or fraction of lines copied) minus
i-io (each omission or error).
Each omission or error counted as one (i).
Any word or words omitted were of course deducted from
the gross number of lines covered to get the figure which was
substituted in the first parenthesis above.
Miscellaneous Arithmetic: The children worked for twenty
minutes each day in Thorndike's booklet "Exercises in Arith-
metic No. 5." Since this test has never been accurately scored
it was of little value for this study, consequently no further men-
tion will be made of it.
Experimental Material and Method 9
TABLE A
Practice Series: Average score made by 88 individuals in the tests
shown at the top on the days shown at the left.
Cop.
Hand-
Add.
Can. 2
Can. 3
Can. A
Can. S
Add.
writing
2/4
32.1
70.1
88.7
26.6
2/5-
37.8
78.5
99.8
35-2
2/8
37.8
85.2
102.7
38.8
2/9
40.2
90.3
105.0
44-4
2/10
41.6
92.7
106.5
47-4
2/ll
44-4
94-9
1 14-5
55-4
42.0
2/lS
430
97-3
1 16.0
54-4
49.0
2/l6
45-4
101.6
118.9
55-2
54-1
2/17
47.9
108.2
123.3
59-3
S8.6
2/l8
50.0
1 10.4
126.9
62.5
63.6
2/19
11.0
7.38
2/23
14.8
6.82
2/24
6.52
Z/25
17.8
7.20
2/26
18.S
7.06
3/1
18.0
6.96
3/2
17.0
6.61
3/3
18.4
6.62
3/4
18.6
6.41
3/S
22.2
6.84
3/6-4/14 Miscellaneous Arithmetic
4/14
46.1
61.3
64.4
21.6
4/15
48.8
64.0
69.9
22.9
4/16
Si-4
70.8
72.6
21.8
4/19
48.1
70.4
73-3
21.0
4/20
50.3
106.9
124.5
22.8
4/21
S3.I
1 10.8
128.3
23.4
4/22
54-1
1 14.9
129.4
24.8
4/23
56.3
122.6
136.0
2S.8
4/26
54-1
125.1
138.7
27.S
4/27
56.4
122.3
1350
25-4
Ill
STATISTICAL TREATMENT OF RESULTS
I. Raw and Corrected Arrays
The net original scores from the tests used in this study are
given in the Appendix. In order that a coefficient of correlation
might be calculated from these original data, it was necessary
to reduce to one figure the many measures obtained from a prac-
tice test. No such reduction was necessary for the data obtained
from the preliminary, final, and special tests, because each of
these was given but once. Further, in order to get a true coeffic-
ient of correlation two measures of every function were necessary
for each individual tested. This was simple in the case of the
preliminary tests. The score made by each child in the pre-
liminary test which was given February 3 was paired with the
score made by the same child in the corresponding final test
given April 28. The ability rank given by one teacher was
paired with the rank of that same child given by the other teacher.
School marks made in arithmetic, geography, and spelling were
totaled and paired with the total of marks made in grammar,
composition, and reading. Omnibus I A and Omnibus I B, being .
so much alike, were combined and paired with the sum of Om-
nibus II A and Omnibus II B. Of the other special measures —
Ruger Proverb and the Age of Reaching the Grade — no second
measure was available. In the case of the practice tests the
scores made by any one child on days i, 3, 5, etc., were added
and averaged. With this was paired the number obtained from
summing and averaging the scores made by that same child on
days 2, 4, 6, etc. The practice test — Cancellation of S's — was
given an odd number of days, so day i was omitted as being
the one most likely to be unreliable.
10
Statistical Treatment of Results ii
An 'array' is simply a column of figures to be correlated
with some other column which permits of pairing by individuals.
These arrays may be measures of the same function or of differ-
ent functions. The preceding paragraph describes the method
used in constructing what may be called the 'raw arrays.' Ob-
viously, many factors may enter to make it impracticable or
impossible to calculate a coefficient of correlation from such ar-
rays. In the case of a practice test, for example, an individual
might be absent on the last few odd days. This would probably
make the first member of the pair smaller than the second. Or,
again, one or more individuals might be absent on a day when a
preliminary, final, or special test was given. Since each of these
tests was given but once, obviously the absent individuals would
have no score at all in that function. Since it was desired that
every test be correlated with every other test, the raw arrays
were examined, and whenever any individual was found who
lacked a score for any preliminary, final, or special test, that
individual was entirely eliminated from this study. Whenever,
in the case of the practice tests, any individual had been absent
more than two odd days or two even days, that individual was
also eliminated. The absences just mentioned refer, of course,
to those days on which the particular test under consideration
was given. Any other absence standard might have been em-
ployed. The more-than-two-days-absent standard seemed to be
the one which would give the maximum accuracy of the scores
with the maximum number of subjects.
But the pairing in arrays was still more refined in the prac-
tice tests. We may take Addition as an example of all of these.
Suppose an individual were absent two days out of the ten odd
days while he was present the ten even days. An average from
the remaining eight odd days would be unduly decreased or in-
creased as compared to the corresponding average from the ten
days, according to whether the two absences were near the be-
ginning or near the end of the practice. In order to overcome
this difficulty, at least in part, the two scores which that individual
would probably have made were padded in. Table A offers a
means for determining this probability for any day in the prac-
tice. From Table A was calculated the average per cent of
each day's increase or decrease with respect to the preceding day.
12 Correlation of Psychologies and Educational Measurements
Using this per cent, the score which would probably have been
made on the day when the individual was absent, was calculated
from the last score made before or the first score made after the
absence. Table B gives the raw arrays for all the tests used for
the entire eighty-eight subjects. By eliminating the individuals
who were absent on single-test days and also those who were
absent more than two odd or two even days for any one practice
test, the eighty-eight subjects were reduced to sixty-three sub-
jects. When the two or less absent days were filled in with the
probable scores. Table C resulted. Let us call Table C the
'corrected arrays.'
In closing this discussion one further remark is necessary. The
original intention was to use more special tests than are shown
in Table B. While these were dropped later, they figured in
the elimination of pupils. Still another fact must be noticed. The
teachers, who gave their opinion of the children's mental ability,
ranked them in order from one to eighty-eight. When many
individuals were eliminated gctps occurred in their ranks. It was
decided to close up these gaps and make the range from one to
sixty-three.
TABLE B
Raw Arrays: Scores or average scores made by 88 children in the
tests shown at the top of each column. Under the practice tests : Column
I = average from odd days ; column 2 = average from even days ; figure
to left of a parenthesis := total score from number of tests shown in the
parenthesis.
[nd.
Additi
ion
Cancelling 2
Cancelling 3
10 tests
10 tests
8 tests
8 tests
8 tests
8 tests
1
2
1
2
1
2
1
102.7
105.7
138.0
142.0
153.5
160.0
2
38.3
356.0[9]
92.3
696.0[7]
111.5
804.017]
3
71.1
71.9
98.8
105.5
117.5
119.5
4
36.0
38.7
87.3
91.8
103.5
106.1
5
261.0[9]
268.018]
720.017]
724.017]
120.8
897.0[7]
e
348.0[9]
356.019]
134.0[1]
7
42.1
45.9
680.0C7]
92.0
105.0
110.3
8
30.0
264.0[8]
80.3
54.218]
102.3
896.016]
9
-56.5
68.5
132.0
136.5
133.3
135.8
10
9.8
12.0
70.0
74.0
92.0
104.8
11
18.4
16.S
98.5
111.8
840.0171
864.017]
12
120.0M]
125.016]
662.0[6]
692.016]
814.0[6]
814.0C6]
13
91.3
94.9
130.3
138.9
157.5
182.6
14
71.4
76.4
113.8
119.0
121.8
120.5
15
27.8
31.8
105.3
106.0
138.0
132.0
18
47.0
49.8
752.017]
115.0
125.8
878.017]
17
28.3
266.019]
96.0
728.017]
115.5
822.017]
18
81.4
64.6
875
96.5
103.8
105.5
19
80.7
84.7
93.5
94.0
101.5
748.017]
20
57.6
63.3
95.5
106.3
123.6
124,9
21
23.9
26.5
111.8
114.3
120.5
125.3
22
268.0E9]
315.019]
682.017]
650.017]
744.017]
747.017]
Statistical Treatment of Results 13
[nd.
Addition
Cancelling 2
Cancelling 3
10 tests
10 tests
8 tests
8 tests
8 tests
8 tests
1
2
1
2
1
2
23
64.3
64.9
100.0
107.3
114.8
124.5
24
50.8
612.0[9]
105.5
102.9
122.0
860.0[7]
25
228.0[5]
270.0[5]
524.0C6]
492.0 [5]
595. 0[5]
626.0[S]
26
51.1
50.4
84.0
91.8
99.8
106.3
27
57.4
68.7
100.8
113.8
113.0
116.3
28
194.0[9]
23.0
97.5
103.8
117.8
124.8
29
36.2
36.5
124.0
112.9
133.0
138.3
30
527.0C9]
56.4
530. 0[7]
76.8
664.0C7]
92.5
31
14.5
14.7
82.3
83.8
101.6
106.3
32
42.5
44.1
780.0C7]
111.8
122.8
125.3
33
66.2
68.5
118.0
122.0
132.8
139.8
34
149. 0[3]
160.0[3].
250.0 [3]
268.0[3]
314.0[3]
238.0[2]
3S
40.2
40.3
78.5
86.8
98.3
101.8
30
24.9
223.0C9]
93.3
710.0L7]
107.4
826.0[7]
37
64.6
70.4
100.8
110.4
806.0 [7]
842. om
38
20.6
201. 0[9]
82.8
34.3
97.5
100.3
39
62.7
63.2
88.8
90.3
111.3
112.0
40
34.0[1]
78.0[2]
66.0[1]
170.0E2]
87.0C1]
204.0[2]
41
36.5
37.8
83.0
85.0
93.0
92.3
42
634.0C9]
692.01:8]
674.0C7]
618.0C6]
802. om
704.0L6]
43
70.8
76.0
94.5
98.8
113.3
113.0
44
33.1
33.7
122.3
120.8
132.0
135.5
50
39.2
41.6
134.3
143.3
1024.0[7]
160.8
51
86.8
82.9
422.0E7]
56.0
62.0
79.8
52
66.9
66.8
62.0
64.3
67.0
74.3
53
250.0[8]
260.0C8]
880.0[6]
128.0[6]
192.0C6]
178.0E6]
54
60.6
53.7
150.6
145.5
148.3
1079.0L7]
55
37.1
40.0
93.8
96.5
116.0
121.3
56
207. Ot8]
221.0E9]
794.0[7]
810.0[6]
832.0C6]
902.0[6]
57
21.9
211.0C9]
58.3
546.0[7]
89.3
94.8
53
64.5
70.9
104.1
109.0
116.4
121.4
59
42.9
45.2
82.0
84.0
116.3
122.5
60
23.9
26.3
87.5
90.3
99.3
660.0[7]
61
27.0
257.0[9]
94.3
106.5
103.9
101.3
62
89.2
94.8
116.0
119.5
129.3
132.9
63
31.6
28.2
98.6
108.3
125.5
129.3
64
284.0[9]
263.0[9]
89.8
640.0[7]
104.8
740. 0[7]
65
226.0C8]
242.0C8]
662.0[7]
594.0E6]
764.0B]
660.0L6]
66
57.2
69.3
87.0
88.3
108.0
108.5
67
48.0
51.9
127.5
133.8
146.3
149.3
68
501.0[9]
445.0[8]
470.0[6]
494.0W]
564.016]
602.0[6]
69
66.0L2]
[0]
170.0E2]
170.0[2]
276.0C3]
204.0C2]
70
29.9
30.9
78.5
85.3
692.0[7]
106.5
71
405.0[9]
46.3
720.0C7]
102.0
822.0E7]
126.3
72
87.9
90.8
103.3
105.8
115.0
121.3
73
40.6
43.7
118.9
125.6
129.0
136,5
74
22.7
24.6
93.3
97.8
736.0C7]
107.0
75
29.3
27.3
142.8
139.5
141.8
148.5
76
50.5
56.8
112.8
126.3
128.3
136.3
77
22.4
24.3
120.3
130.0
1098.0[7]
169.1
78
40.6
42.0
82.3
91.5
102.8
111.0
79
708.0[9]
80.8
752.0m
114.1
900. 0[7]
129.3
80
93.8
.99.4
722.0t7]
736.0m
106.3
117.0
81
65.6
66.6
111.5
120.3
132.0
132.3
82
44.9
429.0B]
113.1
732.0C6]
132.5
980.0m
83
277.0C8]
283.0C6]
568.0W]
646.0[6]
690.0K]
645.0[e
84
39.7
40.8
136.0
141.0
151.5
1063.0[7
85
151.0L5]
204.or6]
272.0 [4]
364.0C5]
378. 0[4]
404.0[4
86
19.9
19.3
102.0
101.8
118.0
118.5
87
29.4
303. 0[9]
108.0
110.8
130.5
138.8
88
26.7
27.9
82.8
90.3
87.8
97.8
89
264.0C4]
197.0[3]
350. 0[4]
298.0C3]
454.0M
332.0[3]
90
63.0
54.8
134.0
131.0
138.6
145.8
91
40.3
368.0[8]
102.3
724.0E7]
131.5
958.om
92
45.4
416.0[9]
89.0
91.3
109.5
111.8
93
423.019]
439.0[9]
572.0[7]
484.0[e]
708.0[7]
804.0[7I
14 Correlation of Psychological and Educational Measurements
TABLE B {continued)
Ind.
Cancelling A
Cancelling S
Copying Addresses
7 tests
7 tests
4 tests
4 tests
10 tests
10 tests
1
2
1
2
1
2
1
54.6
65.7
65.5
73.6
19.6
18.3
2
42.0
298.0L6]
52.0
60.0
22.5
230.0L9]
3
47.3
50.3
43.3
46.0
16.3
18.2
4
50.9
54.1
63.0
65.5
14.7
16.6
S
300.0[6]
270.0C5]
210.0[3]
226.0[3]
22.1
188.0[8]
6
252.0[6]
275.0[6]
-5.0
86.0[3]
11.8
117.0L9]
7
43.7
56.6
40.0
35.0
13.5
15.8
8
45.1
277.0[5]
67.3
60.0
23.5
25.4
9
404.0C5]
444.0C6]
78.0
77.0
21.0
23.0
10
39.4
46.0
51.0
66.3
14.9
16.5
11
51.9
338.0K]
49.5
148.0[3]
21.4
245.0C9]
12
303.0E5]
342.0[5]
126.0[2]
164.0C2]
68.0C5]
89.0L6]
13
69.1
70.0
61.0
66.0
26.8
28.4
14
58.0
68.9
76.3
80.6
17.1
17.6
15
88.1
87.7
85.5
83.0
17.4
19.3
16
57.1
58.1
65.3
70.8
19.0
20.1
17
29.4
36.1
34.5
44.5
16.6
157.0[9]
18
53.7
56.6
59.0
62.5
22.3
25.2
19
49.4
51.9
60.0
52.5
17.4
19.4
20
46.6
46.6
71.8
77.5
22.1
22.8
21
56.0
58.0
77.5
77.5
13.8
14.6
22
298.DM]
46.3
84.0
78.3
18.5
160.0 9]
23
54.0
51.4
66.0
66.5
17.4
187.0 9
24
70.6
432.0[6]
93.6
284.0[3]
26.3
246.0 9
25
269.0C5]
304.0E5]
128.0t2]
146.0[2]
91.0[6]
96.0 5
26
376.0[6]
65.1
76.5
75.5
20.6
22.4
27
60.6
68.3
72.0
64.5
28.9
29.3
28
250.0[6]
44.6
160.0[3]
68.0
146.0L9]
18.5
29
69.7
324.0[6]
73.5
74.5
26.6
28.9
30
268.0[6]
37.7
68.5
64.0
26.5
25.7
31
38.6
232.0[6]
60.5
62.5
158.0[9]
16.5
32
49.4
62.4
71.5
66.5
23.1
23.5
33
72.9
71.7
57.0
62.0
16.6
15.3
34
132. 0[3]
154.0[3]
[0]
[0]
[0]
[0]
35
40.9
41.4
65.0
69.5
20.8
23.2
36
36.9
40.6
18.5
108.0[3]
17.0
168.0[9]
37
80.6
90.9
82.0
87.0
21.1
21.7
38
41.7
38.6
62.0
56.5
15.6
16.0
39
41.7
46.0
77.5
81.0
18.5
20.2
40
0[1]
36.0[2]
[0
[0]
[0]
[0]
41
60.3
50.6
132.013
51.5
18.9
18.8
42
318.0L6]
358.0[5]
145.0L2
228. 0t3]
29.7
28.1
43
58.3
58.3
63.5
64.6
17.5
16.8
44
75.4
73.4
68.5
67.0
148.0W]
182.0[9]
60
66.4
65.4
76.8
86.0
25.3
249.0[9]
SI
45.4
55.4
39.8
157.0[3]
21.8
23.3
52
31.1
33.1
42.0
44.0
14.7
142.0[9]
53
280.0[6]
316.0C6]
178.0E3]
200.0C3]
178.0[8]
210.0[9]
54
66.9
73.0
49.0
55.5
22.6
23.1
55
34.9
44.9
51.5
49.5
16.2
19.1
56
356.0K]
58.3
80.5
82.0
184.0E9]
203. 0[9]
57
44.6
46.3
52.5
59.5
17.4
18.0
58
66.3
70.9
68.5
69.3
21.5
23.0
59
39.7
44.9
72.0
76.0
18.1
18.8
60
42.3
43.7
48.5
63.0
19.1
19.1
61
48.9
334.0[e]
66.0
204.0[3]
14.4
i3o.o[g]
62
66.0
60.3
69.8
76.0
23.5
24.4
63
64.6
62.0
65.5
66.5
17.3
16.2
64
267.0C6]
49.7
170.0E3]
62.0
204.0[9]
204.0[9]
65
44.3
47.7
43.5
69.0
113.0[9]
88.017]
66
36.1
42.0
68.0
71.0
15.0
16.7
67
43.7
48.0
60.5
61.8
18.5
19.9
68
206.0[5]
210.0C6]
166.0[3]
174.0[3]
175.0[9]
21.3
fl9
100.0[3]
84.0[2]
26.0C1]
[0]
[0]
[0]
70
50.9
54.9
49.6
63.5
19.9
22.4
71
58.1
56.7
66.0
68.5
164.0C9]
19.9
72
51.7
53.7
63.0
60.0
20.5
22.6
73
53.7
58.3
73,0
212.0C3]
14.1
15.9
74
43.1
48.9
68.0
68.0
17.8
18.8
75
76.3
87.3
89.3
91.5
18.8
20.5
76
60.3
55.7
64.6
70.0
29.8
29.9
77
57.4
56.9
71.0
77.0
22.7
23.5
78
41.4
43.7
46.0
64.5
19.5
20.7
Statistical Treatment of Results
15
[nd.
Cancelling A Cancelling S
Copying Addresses
7 tests 7 tests 4 tests
4 tests
10 tests
10 tests
1 2 1
2
1
2
79
—31.1 —28.6 26.0
27.0
178.0C9]
187.0[9]
80
52.1 54.4 62,5
61.0
21.9
23.0
81
82
83
81
85
36
87
79.1 83.1 66.5
68.9 432.0B] 44.5
226.0C5] 268.0[5] 164.0[2]
56.6 66.0 62.5
26.0[1] 156.0[3] 32.0E1]
58.6 59.4 66.0
45.1 339.0E6] 68.0
'
69.5
176.0[3]
164.0[2]
78.5
200.0[3]
67.5
194.0L3]
30.5
22.0
202.0[9]
19.9
102.0E7]
16.1
17.5
32.5
24.7
206.0C9]
22.6
130.0[7]
16.3
167.0C9]
88
41.7 42.9 51.5
59.0
13.6
15.3
89
90
91
186.0M 168.0L3] 60.0[1]
72.3 83.1 86.0
324.0C6] 322.0E5] 252.0E3]
[0]
94.0
264.0[3]
[0]
21.9
178.0C9]
[uj
24.7
194.0E9]
92
«3
43:1 278.016] 184.0C3]
65.6 69.7 61.0
182.0[3]
I84.0[3]
22.2
171.0[8]
207.019]
211.0[9]
Ind.
Handwriting
Visual
10 tests 10 tests
Vocabulary
Completion
1 2
1
2
1
i
1
6.38 6.42
12
21
30
17
37
23
24
24
16
26
36
24
25
32
35
26
28
2
7.27 60.00LS]
14
13
39
3
7.60 6.99
25
21
29
4
6.04 6.15
20
26
29
5
7.11 58.2018]
17
20
32
6
6.15 48.40C8]
33
37
8
7
6.66 6.79
30
27
31
g
4.57 4.38
11
24
38
9
7.68 7.17
24
21
27
10
5.55 6.68
18
24
38
11
5.87 5.62
14
15
26
12
13
65.60[8] 7.55
9.43 9.19
19
21
22
30
38
27
14
6.52 6.61
13
6
27
15
4.65 4.50
25
29
28
30
27
38
32
16
7.22 6.88
11
23
19
17
4.89 4.88
14
20
38
18
6.19 6.34
11
21
29
19
6.51 6.42
16
33
26
26
20
6.75 6.35
17
24
30
31
21
5.97 6.57
20
29
27
28
22
6.99 7.34
14
21
34
31
23
6.41 6.99
15
18
25
31
24
6.31 5.95
15
21
30
29
25
26
6.08 6.26
5.85 6.97
15
20
21
33
28
29
27
7.90 7.97
4
14
43
46
28
7.02 7.07
13
21
36
25
29
7.29 7.30
13
23
24
31
30
4.90 43.00[8]
16
17
28
33
31
47.60C8] 5.87
10
22
31
28
32
8.42 8.72
14
22
30
30
33
e.60 6.55
12
—
36
27
34
35
[0] [0]
6.98 7.35
12
5
10
36
47
41
36
7.94 7.56
29
27
25
25
37
7.03 6.78
20
26
30
30
38
4.92 4.94
18
19
30
30
39
6.35 6.07
13
21
29
30
46
41
[0] , [0]
7.47 7.07
24
8
17
22
38
36
42
7.94 6.79
14
19
30
33
43
44
6.63 9.61
21
22
23
—
43.30[6] 42.00t6]
16
23
25
28
50
8.59 8.23
20
28
28
27
51
6.70 6.65
13
16
38
32
52
5.43 44.50[8]
18
31
27
30
53
50.00C8] 6.73
19
25
31
25
64
55
7.24 7.59
30
27
28
26
5.76 6.44
14
21
24
26
56
9.61 8.98
15
—
31
—
57
58
59
60
5 25 4.99
14
20
32
29
6.49 6.57
21
23
28
27
7.31 6.68
13
24
32
34
6.83 6.72
18
33
25
20
1 6 Correlation of Psychological and Educational Measurements
TABLE B (continued)
Ind.
Handwriting
Visual
10 tests
10 tests
Vocabulary
Completior
I
1
2
1
2
1
2
61
5.16
5.07
15
26
29
28
62
7.33
7.62
12
15
33
37
83
6.43
6.78
18
29
30
30
64
7.03
6.92
6
39
—
65
7.89
63.00t8]
7
28
19
22
66
7.12
7.30
16
24
27
28
67
7.87
8.32
19
30
25
25
6S
7.72
8.66
9
13
43
69
tO]
[0]
36
26
70
6.99
7.13
22
28
29
27
71
6.58
6.19
18
23
31
30
72
7.10
6.91
14
22
38
32
73
7.06
7.08
16
33
22
20
74
6.03
6.88
16
23
30
25
7S
8.21
8.06
24
25
22
20
76
9.41
8.93
14
24
30
33
77
7.15
7.35
15
24
29
78
5.60
5.45
14
21
36
35
79
6.62
6.60
16
33
28
23
80
8.14
7.85
11
17
42
42
81
9.47
9.60
12
20
38
37
82
7.41
7.47
17
30
37
33
83
63.70C8]
60.80[8]
9
22
36
28
84
6.29
6.62
11
21
31
33
85
36.10[6]
37.30t6]
16
24
34
30
86
6.90
7.04
16
18
25
28
87
6.17
6.46
20
31
19
33
88
5.63
5.91
14
26
29
28
89
[0]
[0]
20
33
90
7.23
7.47
21
19
22
30
91
7.35
7.39
23
20
28
92
8.42
8.41
12
16
34
36
93
60.10C8]
7.32
16
23
31
23
nd.
Arithmetic
Reading
Omnibus I
A
B
1
2
1
2
1
2
1
1
5
21
24
41.0
41.0
2
4
6
30
36
20.0
19.0
3
4
5
23
28
42.5
39.5
4
2
2
27
27
43.0
46.0
6
4
2
24
31
30.0
30.0
6
1
1
17
12
66.0
64.0
7
2
2
19
16
43.0
43.6
8
6
4
29
28
29.6
22.6
9
6
5
29
16
32.0
39.6
10
2
2
22
31
37.5
43.0
11
4
4
31
37
32.0
47.6
12
4
6
27
43
30.0
28.0
13
4
3
18
26
32.0
41.0
14
3
4
21
23
46.0
43.0
15
1
1
26
28
32,0
31.6
16
6
3
31
32
39.0
42.0
17
2
29
28
44.6
44.0
18
3
2
28
32
27.5
26.0
19
3
4
26
28
36.5
35.0
20
2
4
21
33
20.6
34.5
21
1
2
26
31
54.0
44.0
22
5
3
28
31
34.0
40.0
23
4
4
24
37
25.0
32.0
24
2
4
29
34
31.5
27.0
26
2
—
29
—
31.6
26
2
4
24
26
30.0
39.0
27
4
5
32
43
7.5
19.5
28
1
3
26
27
39.6
24.0
29
4
4
23
36
50.0
42.0
30
3
3
26
31
26.6
25.6
31
4
3
27
28
44.0
29.5
32
1
2
26
39
17.6
29.0
33
2
—
27
28
42.6
33.0
34
2
—
26
—
26.0
Statistical Treatment of Results 17
Ind.
35
36
37
38
39
40
41
42
43
44
SO
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
89
90
91
Ind.
1
2
3
4
S
9
7
8
6
10
11
12
13
14
15
16
17
18
19
Arithmetic
Reading
A
1
mnibus 1
1
2
1
2
2
5
3
31
46
10.5
16.0
5
2
25
21
51.0
44.0
1
3
27
26
28.5
25.5
5
4
25
37
42.5
30.5
4
4
25
33
27.0
33.5
20
36.0
5
4
25
41
1S.5
4.5
4
3
26
40
18.0
30.0
4
4
28
—
32.0
4
3
24
38
33.0
30.0
2
1
22
22
34.0
35.0
3
5
28
35
28.0
13.5
3
4
27
32
42.0
30.0
4
4
23
31
38.0
34.5
2
3
21
19
43.0
37.0
4
4
28
37
28.5
36.5
2
23
31.0
4
3
30
41
30,0
33.0
3
3
24
30
51.5
27.5
2
3
26
33
22.5
35.0
5
2
30
28
40.5
35,0
1
4
26
28
55.5
25.0
3
4
25
39
28.5
19.5
1
3
25
25
69.5
44.0
3
30
9.0
8.0
3
2
24
20
69.0
53.0
1
3
25
40
26.0
34.0
1
3
24
26
31.5
35,5
5
4
28
18.5
17.0
2
27
SO.O
4
3
23
33
30.0
26.5
2
4
26
34
28.0
30.0
6
6
25
34
17.0
24.5
2
4
25
22
39.5
44.0
5
5
27
31
35.0
26.5
4
3
23
33
48.0
49.0
2
4
22
36
37.0
34.0
2
2
21
36.0
26.0
4
5
23
is
28.5
30.5
4
1
25
15
59.0
64.0
6
5
25
40
28.5
16.0
5
3
28
45
23.0
13.5
3
3
27
28
29.5
17.0
3
21
32
28.0
41.0
2
4
27
32
34.5
24.5
5
5
29
43
27.0
27.0
1
3
28
33
34.5
23.0
1
S
25
35
38.5
30.0
3
5
29
37
37,5
23.0
5
24
— .
34.0
1
4
9
27
38.0
39.5
3
2
28
35.5
45.0
4
4
23
38
25.5
31.0
3
5
26
27
36.5
38.5
Omnib'
us II
Proverb
Teacher Rank
Age in months
A
B
1
2
1
2
89.5
78.0
2
64
S3
155
45.0
45.5
4
39
28
153
71.0
73.5
3
29
41
145
82.0
63.0
2
72
71
153
63.0
52.5
10
25
30
155
94.0
82.0
3
88
88
172
69.5
65.5
2
80
80
156
39.0
60.0
6
16
14
137
69.6
63.5
2
33
20
161
64.6
62.0
1
42
36
163
75.0
68.5
4
37
54
153
87.0
51.0
—
44
44
173
82.0
76.0
4
50
49
136
82^0
85.0
6
82
84
148
82.0
73.5
3
41
48
134
910
66.5
S
70
81
166
79!
53.0
65.5
59.5
48.5
70.5
1
3
64
13
76
69
29
68
159
137
165
i8 Correlation of Psychological and Educational Measurements
TABLE B (^continued)
Omnibus 11
Proverb
Teacher Rank
Age in moi
Ind.
A
B
1
2
1
2
20
80.0
58.6
3
66
63
144
21
84.5
64.6
1
61
61
139
22
81.0
53.5
66
67
163
23
54.0
43.0
5
26
18
145
24
78.0
47.0
4
10
11
143
25
49.5
7
8
145
26
79.0
68.0
3
78
82
182
27
34,5
22.0
11
1
4
139
28
76.0
57.5
3
84
76
155
29
81.0
63.0
7
20
26
154
30
42.0
54.0
2
31
39
150
31
78.0
65.0
3
46
45
162
32
69.0
59.5
4
65
60
162
33
82.5
61.0
2
67
79
167
34
51.0
—
60
62
152
35
39.0
40.0
11
4
5
164
36
76.0
74.0
— .
71
57
143
37
70.5
31.6
6
30
26
161
38
75.5
60.0
6
52
34
142
39
60.9
44.6
2
18
37
150
40
101.5
—
63
66
166
41
69.0
39.0
11
3
1
154
42
52.0
72.0
4
22
23
147
43
73.0
5
36
32
146
44
64.0
51.0
7
48
31
141
50
76.5
70.0
5
59
55
146
51
47.5
44.5
3
16
9
140
52
67.0
64.0
4
35
33
150
53
86.5
55.0
—
40
46
147
54
90.5
77.0
1
86
86
163
55
60.0
63.5
6
68
40
153
56
91.5
4
81
73
183
57
64.5
32.0
1
38
56
147
58
80.5
65.0
4
9
13
135
59
76.0
73.0
10
45
38
160
60
31.5
75.5
3
75
65
166
61
89.5
72.0
5
43
51
137
62
50.0
43.0
5
14
6
162
63
78.0
61.6
2
69
83
156
64
34.0
34.5
13
12
32
146
65
118.0
89.0
—
87
85
196
66
63.0
60.0
5
51
52
154
67
86.0
72.0
4
74
77
155
63
36.0
39.0
13
8
12
138
69
67.0
—
83
73
166
70
36.5
65.0
5
24
43
133
71
82.0
61.5
2
49
59
140
72
53.0
42.5
9
19
7
151
73
79.0
67.5
5
79
68
180
74
76.0
62.5
4
11
15
142
75
83.0
55.0
3
67
60
158
76
80.5
73.6
4
47
21
151
77
72.6
67.0
8
32
35
141
78
60.5
64.5
2
21
22
140
79
80.5
86.0
—
86
87
154
80
41.5
36.0
7
6
2
142
81
47.5
46.5
2
2
3
146
82
49.5
55.5
11
5
10
132
83
80.5
62.0
2
73
70
155
84
79.5
63.6
8
56
64
143
85
57.5
33.5
4
23
42
151
86
84.0
65.0
1
68
75
148
87
73.0
61.5
5
17
24
137
83
66.0
68.0
7
34
25
144
89
64.0
—
62
16
138
90
94.0
83.5
4
S3
47
150
91
73.6
64.6
3
77
74
182
92
62.0
53.6
9
27
17
150
93
64.0
66.6
4
23
19
154
Statistical Treatment of Results 19
TABLE C
Corrected Arrays: Scores or average scores made by 63 children in
the tests shown at the top of the column. Under the practice tests :
Column I = average score from odd days ; column 2 = average score
from even days. The number of days is shown at the top. B = boy;
G = girl.
Ind. Addition Cancelling 2 Cancelling 3
10
10
8
8
8
8
tests
tests
tests
tests
tests
tests
1
2
1
2
1
2
IB.
102.7
105.7
138.0
142.0
153.5
160.0
2B.
38.3
38.7
92.3
98.1
111.5
113.3
3B.
71.1
71.9
98.8
105.5
117.5
119.5
4G.
36.0
38.7
87.3
91.8
103.5
106.1
7G.
42.1
45.9
79.4
92.0
105.0
110.3
9B.
56.5
58.5
132.0
136.5
133.3
135.8
lOB.
9.8
12.0
70.0
74.0
92.0
104.8
UB.
18.4
16.5
98.6
111.8
121.0
124.5
13B.
91.3
94.9
130.3
138.9
157.6
162.5
14B.
71.4
76.4
113.8
119.0
121.8
120.5
15G.
27.8
31.8
106.3
106.0
138.0
132.0
16B.
47.0
49.8
108.3
115.0
125.8
125.4
18G.
61.4
64.6
87.5
96.5
103.8
105.5
19G.
80.7
84.7
93.5
94.0
101.5
104.8
20G.
67.6
63.3
96.5
106.3
123.6
124.9
21G.
23.5
26.5
111.8
114.3
120.5
125.3
23B.
54.3
54.9
100.0
107.3
114.8
124.5
24G.
50.8
57.3
106.5
102.9
122.0
124.0
26G.
51.1
50.4
84.0
91.8
99.8
106.3
27G.
57.4
58.7
100.8
113.8
113.0
116.3
28G.
21.S
23.0
97.5
103.8
117.8
124.8
29B.
36.2
36.5
124.0
112.9
133.0
138.3
30B.
53.2
66.4
73.6
76.8
90.0
92.5
31B.
14.5
14.7
82.3
83.8
101.5
105.3
32B.
42.5
44.1
108.6
111.8
122.8
125.3
35B.
40.2
40.8
76.5
86.8
98.3
101.8
37G.
64.6
70.4
100.8
110.4
117.2
120.5
38B.
20.6
22.0
82.8
84.3
97.6
100.3
39G.
52.7
63.2
88.8
90.3
113.3
112.0
41B.
35.5
37.8
83.0
85.0
93.0
92.3
42B.
70.2
74.8
97.6
96.6
113.9
113.8
SOG.
39.2
41.6
134.3
143.3
144.0
150.8
51G.
86.8
82.9
64.6
66.0
62.0
79.8
52G.
66.9
65.8
62.0
64.3
67.0
74.3
54G.
S0.6
53.7
150.5
145.5
148.3
150.9
55B.
37.1
40.0
93.8
96.5
116.0
121.3
57G.
21.9
23.4
68.3
74.1
89.3
94.8
58B.
64.5
70.9
104.1
109.0
116.4
121.4
S9B.
42.9
46.2
82.0
84.0
116.3
122.6
60B.
23.9
26.3
87.6
90.3
99.3
95.4
61B.
27.0
28.4
94.3
106.5
103.9
101.3
62B.
89.2
94.8
115.0
119.5
129.3
132.9
63G.
31.6
28.2
98.5
108.3
125.5
129.3
66B.
57.2
59.3
87.0
88.3
108.0
108.5
678.
48.0
51.9
127.5
133.8
145.3
149.3
70G.
29.9
30.9
78.5
85.3
98.3
106.5
71B.
45.0
45.3
106.6
102.0
120.1
126.3
72B.
87.9
90.8
103.3
105.8
116.0
121.3
73B.
40.6
43.7»
118.9
125.5
129.0
136.6
74G.
22.7
24.6
93.3
97.8
106.8
107.0
7SG.
29.3
27.3
142.8
139.5
141.8
148.5
76B.
50.5
65.8
112.8
126.3
128.3
136.3
78B.
40.6
42.0
S2.3
91.5
102.8
111.0
SOB.
93.8
99.4
97.4
104.0
106.3
117.0
82G.
44.9
47.7
113.1
119.8
132.6
138.7
83G.
33.6
34.5
94.9
95.6
113.7
108.9
84G.
39.7
40.8
136.0
141.0
151.5
155.4
86G.
19.9
19.3
102.0
101.8
118.0
118.5
87G.
29.4
33.4
108.0
110.8
130.5
138.8
88B.
26.7
27.9
82.8
90.3
87.8
97.8
90B.
53.0
54.8
134.0
131.0
138.6
145.8
92B.
45.4
47.1
89.0
91.3
109.6
111.8
93B.
48.5
49.0
82.5
82.5
104.8
116.7
Av.
= 47.1
49.2
99.8
104.1
115.6
119.8
20 Correlation of Psychological and Educational Measurements
TABLE C {continued)
Copying
Cancelling A Cancelling S Addresses Handwriting
7 7 4 4 10 10 10 10
Ind. tests tests tests tests tests tests tests tests
1
2
1
2
1
2
1
2
IB.
S4.6
65.7
65.5
73.5
19.6
18.3
6.4
fl.4
2B.
42.0
47.8
52.0
60.0
22.5
24.9
7.3
7.3
3B.
47.3
50.3
43.3
46.0
16.3
18.2
7.8
7.0
IG.
50.9
54.1
63.0
65.5
14.7
16.6
6.0
«.2
7G.
43.7
56.6
40.0
35.0
13.5
15.8
6.7
8.8
SB.
71.9
77.3
78.0
77.0
21.0
23.0
7.6
7.2
lOB.
39.4
46.0
61.0
65.3
14.9
16.5
6.6
5.7
IIB.
51.9
56.2
49.5
501
21.4
26.2
5.9
6.6
13B.
69.1
70.0
61.0
66.0
25.8
28.4
9.4
9.2
14B.
58.0
58.9
75.3
80.5
17.1
17.6
6.5
8.6
150.
88.1
87.7
86.5
83.0
17.4
19.3
4.7
4.5
16B.
57.1
58.1
65.3
70.8
19.0
20.1
7.2
6.9
18G.
53.7
56.6
69.0
62.5
22.3
25.2
6.2
8.3
19G.
49.4
51.9
60.0
52.5
17.4
19.4
6.5
6.4
20G.
46.6
46.6
71.8
77.5
22.1
22.8
6.8
8.4
21G.
56.0
58.0
77.5
77.5
13.8
14.6
6.0
6.6
23B.
54.0
51.4
66.0
66.5
17.4
19.7
6.4
6.0
24G.
70.6
74.7
93.5
97.8
26.3
30.6
6.3
6.0
26G.
59.2
65.1
75.5
75.5
20.5
22.4
5.9
8.0
27G.
60.6
68.3
72.0
64.5
28.9
29.3
7.9
8.0
28G.
43.6
44.6
53.6
58.0
16.4
18.5
7.0
7.1
29B.
59.7
58.7
73.5
74.5
26.6
28.9
7.3
7.3
30B.
39.7
37.7
68.5
64.0
26.5
25.7
4.9
S.4
31B.
38.6
40.2
605
62.5
17.2
16.5
5.0
5.9
32B.
49.4
52.4
71.5
66.5
23.1
23.5
8.4
8.7
35B.
40.9
41.4
55.0
69.5
20.8
23.2
7.0
7.4
37G.
80.6
90.9
82.0
87.0
21.1
21.7
7.0
6.8
38B.
41.7
38.6
52.0
56.5
15.6
16.0
4.9
4.9
39G.
41.7
46.0
77.5
81.0
18.5
20.2
8.4
6.1
41B.
S0.3
60.6
43.3
51.5
18.9
18.8
7.5
7.1
42B.
55.0
60.0
51.3
61.5
29.7
28.1
7.9
6.8
50G.
65.4
65.4
76.8
86.0
25.3
27.3
8.8
8.2
61G.
46.4
55.4
39.8
52.9
21.8
23.3
6.7
6.7
62G.
31.1
33.1
42.0
44.0
14.7
14.4
5.4
6.5
{4G.
56.9
73.0
49.0
56.5
22.6
23.1
7.2
7.6
5SB.
34.9
44.9
51.5
49.6
16.2
19.1
6.8
6.4
57G.
44,6
46.3
52.5
59.5
17.4
18.0
5.3
5.0
S8B.
65.3
70.9
68.5
69.3
21.5
23.0
6.5
8.6
59B.
39.7
44.9
72.0
76.0
18.1
18.8
7.3
6.7
eoB.
42.3
43.7
48.5
63.0
19.1
19.1
6.8
6.7
61B.
48.9
55.4
66.0
69.5
14.4
15.7
5.2
5.1
628.
56.0
60.3
69.8
76.0
23.5
24.4
7.3
7.6
63G.
64.8
62.0
65.5
66.5
17.3
16.2
5.4
5.8
eoB.
35.1
42.0
68.0
71.0
15.0
16.7
7.1
7.3
67B.
43.7
48.0
60.5
61.8
18.5
19.9
7.9
8.3
70G.
50.9
64.9
49.5
53.5
19.9
22.4
7.0
7.1
7IB.
58.1
66.7
66.0
68.5
21.3
19.9
5.6
6.2
72B.
51.7
53.7
53.0
60.0
20.5
22.6
7.1
8.9
73B.
63.7
58.3
73.0
73,7
14.1
15.9
7.1
7.1
74G.
43.1
48.9
68.0
68.0
17.8
18.8
8.1
6.9
75G.
76.3
87.3
89.3
91.6
18.8
205
8.2
8.1
7eB.
50.3
55.7
64.5
70.0
29.8
29.9
9.4
8.9
78B.
41.4
43.7
46.0
64.5
19.5
207
5.6
5.5
SOB.
52.1
54.4
62.5
61.0
21.9
23.0
8.1
7.9
82G.
68.9
73.3
44.5
56.1
22.0
24.7
7.4
7.5
83G.
46.3
52.7
74.3
77,4
21.0
22.3
6.8
7.6
84G.
56.6
66.0
62.5
78.5
19.9
22.6
6.3
6.5
86G.
58.6
59.4
66.0
67.5
16.1
16.3
6.9
7.0
87G.
45.1
64.9
58.0
66.2
17.5
18.6
8.2
6.5
88B.
41.7
42.9
51.5
59.0
13.6
15.3
5.6
5.9
90B.
72.3
83.1
86.0
94.0
21.9
24.7
7.2
7.6
92B.
43.1
46.5
68.9
61.7
22.2
23.0
8.4
8.4
93B.
65.6
69.7
61.0
63.4
21.9
23.1
7.5
7.3
Av.
— 62.4
56.7
62.6
85.0
19.8
19.9
8.7
6.8
Statistical Treatment of Results
21
Visual
Ind. Vocabulary
1 2
1 12 21
2 14 13
3 2S 21
4 20 26
7 30 27
9 24 21
10 18 24
11 14 15
13 21 30
14 13 6
15 25 29
16 11 23
18 11 21
19 16 33
20 17 24
21 20 29
23 15 18
24 15 21
28 20 21
27 4 14
28 13 21
29 13 23
30 16 17
31 10 22
32 14 22
35 5 10
37 20 26
38 18 19
39 13 21
41 8 17
42 14 19
50 20 28
61 13 16
62 18 31
64 30 27
65 14 21
87 14 20
68 21 23
59 13 24
60 18 33
61 15 26
62 12 15
63 18 29
66 16 24
67 19 30
70 22 28
71 18 23
72 14 22
73 15 33
74 16 23
75 24 25
76 14 24
78 14 21
80 11 17
82 17 30
83 9 22
84 11 21
86 16 18
87 20 31
88 14 26
90 21 19
92 12 16
93 15 23
Av. =16.1 22.
Completion
Arith.
Readi
ing
1
2
1
2
1
2
30
17
1
5
21
24
39
37
4
5
30
36
29
23
4
5
23
28
29
24
2
2
27
27
31
26
2
2
19
16
27
24
5
5
29
16
38
25
2
2
22
31
26
32
4
4
31
37
27
26
4
3
18
26
27
28
3
4
21
23
28
30
1
1
26
28
19
27
5
3
31
32
29
32
3
2
28
32
26
26
3
4
26
28
30
31
2
4
21
33
27
28
1
2
26
31
25
31
4
4
24
37
30
29
2
4
29
34
28
29
2
4
24
25
43
46
4
5
32
43
36
25
1
3
25
27
24
31
4
4
23
35
28
33
3
3
26
31
31
28
4
3
27
28
30
30
1
2
25
39
47
41
5
3
31
46
30
30
1
3
27
26
30
30
5
4
25
37
29
30
4
4
25
33
38
36
5
4
25
41
30
33
4
3
26
40
28
27
2
1
22
22
38
32
3
5
28
35
27
30
3
4
27
32
28
26
2
3
21
19
24
26
4
4
28
37
32
29
4
3
30
41
28
27
3
3
24
30
32
34
2
3
26
33
25
20
5
2
30
28
29
28
1
4
26
28
33
37
3
4
25
39
30
30
1
3
25
25
27
28
1
3
25
40
25
25
1
3
24
26
29
27
4
3
23
33
31
30
2
4
26
34
38
32
6
6
25
34
22
20
2
4
25
22
30
25
5
5
27
31
22
20
4
3
23
33
30
33
2
4
22
36
35
35
4
5
23
35
42
42
5
5
25
40
37
33
3
3
27
28
36
28
3
21
32
31
33
2
4
27
32
25
28
1
3
28
33
19
33
1
5
25
35
29
23
3
5
29
37
22
30
1
4
9
27
34
36
4
4
23
38
31
23
3
5
26
27
.6 30.
29.4 2.9 3.6
1 25.2
1 31.1
22 Correlation of Psychological and Educational Measurements
TABLE C (continued)
Pro- Age in
id.
Omnibus
verb 1
I'nths '
r'ch'r
Rank
Schoo
IMarl
1
2
1
2
1
2
1
130.5
119.0
2
155
42
41
46
48
2
65.0
64.5
4
153
30
23
55
58
3
113.5
113.0
3
145
22
32
55
51
4
125.0
109.0
2
153
53
64
43
41
7
112.5
109.0
2
156
60
58
41
45
9
101.5
103.0
2
151
25
16
61
51
10
102.0
105.0
1
163
32
27
61
49
11
107.0
116.0
4
153
28
42
49
56
13
114.0
117.0
4
136
38
37
66
56
U
128.0
128.0
6
148
61
62 '
38
31
15
114.0
105.0
3
134
31
36
59
61
16
130.0
108.5
5
166
52
59
38
47
18
80.5
74,5
3
137
9
24
68
71
19
101.0
105,5
3
165
67
52
46
43
20
109.5
93.0
3
144
49
49
57
66
21
138.5
108.5
1
139
48
48
39
47
23
79.0
75.0
5
145
20
13
67
63
24
109.5
74,0
4
143
7
9
76
72
26
109.0
107.0
3
182
58
60
48
41
27
42.0
41.5
11
139
1
3
74
68
28
115.5
81.5
3
155
62
56
42
62
29
131.0
105,0
7
164
16
21
69
52
30
67.5
79,5
2
150
24
30
67
64
31
122,0
94,5
3
152
35
34
50
46
32
76.5
88.5
4
162
43
47
41
55
35
49.5
56.0
11
164
3
4
68
72
37
99.0
570
6
101
23
22
68
58
33
118.0
90,5
5
142
40
26
60
54
39
87.5
78.0
2
150
13
28
67
61
41
74.5
43.5
11
164
2
1
76
76
42
70.0
102,0
4
147
17
18
62
57
50
110.5
106,0
5
146
47
43
55
66
51
75.5
58.0
3
140
11
7
74
69
62
109.0
94.0
4
150
27
25
65
65
54
133.5
114.0
1
163
03
63
36
44
65
88.5
100.0
5
153
46
31
47
46
57
94.5
65,0
1
147
29
44
59
66
58
132.0
92,5
4
135
6
10
72
68
59
98.5
108.0
10
160
34
29
64
59
60
122.0
110,5
3
166
53
51
37
51
61
145.0
97.0
5
137
33
39
55
58
62
78.5
62.5
5
162
10
5
69
73
63
137.5
105.5
2
156
51
61
50
51
66
89.0
94.0
5
154
39
40
62
57
67
117.5
107,5
4
155
55
57
43
50
70
116.5
91,5
5
133
19
33
58
66
71
110.0
91,5
2
140
37
46
58
66
72
70.0
67.0
9
151
14
6
69
69
73
118.5
111.5
5
180
59
45
41
39
74
111.0
89.0
4
142
8
11
66
53
75
131.0
104.0
3
158
45
38
51
50
76
117.5
107.5
4
151
36
16
68
56
78
89.0
95.0
2
140
16
17
67
70
80
70.0
52,0
7
142
5
2
73
77
82
79,0
72.5
11
132
4
8
73
76
83
108.5
142,5
2
155
54
53
39
53
84
114.0
88.0
8
143
44
60
46
66
86
118.5
88.0
1
148
50
55
SO
63
87
111.5
91.5
5
137
12
19
68
70
88
102.5
91.0
7
144
26
20
63
68
90
132.0
123.0
4
150
41
35
52
49
92
87.S
89.5
9
150
21
12
64
S7
93
100.5
105.0
4
154
18
14
65
56
Av.
= 103.8
93.1
4.4
150.3
32.
32.
9S.1
67.4
Statistical Treatment of Results 23
2. Deviations and Their Combination
The next step in calculating the coefficients of correlation was
to turn all the scores in any one column of Table C into plus
and minus deviations from the average shown at the foot of that
column. These deviations are given in Table D. At the foot
of each column is the square root of the sum of the deviations
squared, which we shall find to be useful later. Further it will
be remembered that Visual Vocabulary and the Omnibus tests
were scored in terms of penalties, and what amounts to the same
thing, a small measure by Teacher Rank means large excellence.
To make these tests comparable to the others all their plus de-
viations were changed to minus and all their minus deviations to
plus.
The reader will notice that two new tests appear in this devia-
tion table. For reasons to be considered later it was found
desirable to combine Visual Vocabulary with Completion. Col-
umn I of this new measure is the algebraic sum by individuals of
the deviations of Visual Vocabulary (i) and Completion (2) ;
Column 2 is the sum of Visual Vocabulary (2) and Completion
(i). The second of these tests or measures is a Composite.
Column I of this Composite is an algebraic total by individuals
of all the column I's of all the tests shown in Table E. Column 2
of the Composite is the same thing for all the column 2's. But
contrary to the Visual Vocabulary and Completion combination,
not all the tests in Table E received equal weight. The weight
actually given to each half of each test is shown under "Weight
given," ^ in Table E. These weights were guesses, guided by what
experimental evidence was then available, as to the relative value
of each test as a measure of mental ability. Now the desired
weighting was obtained by multiplying or dividing the deviations
in any one column by the figure under "Multiple" in Table E.
These figures were those which, when divided or multiplied into
the square root of the sum of the deviations squared divided by
ten, changed these square roots to the relative sizes shown under
"Weight given" in Table E. In psychological literature such a
Composite is usually taken as a measure of general mental ability.
1 This weight was given before onr own coefficients were calculated.
24 Correlation of Psychological and Educational Measurements
TABLE D
Deviations from the Average of Each Test
V
Ind.
Addition
Cancelling 2
Cancelling 3
Cancelling A
1
2
1
2
1
2
1
2
1
65.6
66.5
38.2
37.9
37.9
40.2
2.2
9.0
2
-8.8
—10.5
— 7.5
— 6.0
— 4.1
— 6.5
—10.4
— 8.9
3
24.0
22.7
— 1.0
1.4
1.9
-03
— 5.1
— 6.4
4
—11.1
—10:5
—125
—12.3
—12.1
—13.7
-1.5
— 2.6
7
— 5.0
— 3.3
—204
—12.1
-108
-9.5
— 8.7
— 0.1
9
9.4
9.3
32.2
32.4
17.7;
16.0
19.5
206
10
—37.3
—37.2
—29.8
—301
—23.6
—16.0
—13.0
—10.7
11
—28.7
—32.7
— 1.3
7.7
5.4
4.7
— 0.5
-0.5
13
44.2
45.7
305
34.8
41.9
42.7
16.7
13.3
14
24.3
27.2
14.0
14.9
6.2
0.7
5.6
2.2
15
—19.3
—17.4
5.5
1.9
22.4
12.2
35.7
31.0
16
— 0.1
0.6
8.5
10.9
10.2
6.6
4.7
1.4
18
14.3
15.4
—12.3
— 76
—11.8
—14.3
1.3
— 0.1
19
33.6
35.5
— 6.3
—10.1
—14.1
—16.0
— 3.0
— 4.8
20
10.5
14.1
— 4.3
2.2
7.9
5.1
— 5.8
—10.1
21
—23.6
—22.7
12.0
10.2
4.9
5.5
3.6
1.3
23
7.2
5.7
0.2
3.2
— 0.8
4.7
1.6
— 5.3
24
3.7
8.1
5.7
— 1.2
6.4
4.2
18.2
18.0
26
4.0
1.2
—15.8
—12.3
—15.8
—13.5
6.8
8.4
27
10.3
9.5
1.0
9.7
-2.6
-3.5
8.2
11.6
28
—25.3
—26.2
— 2.3
— 0.3
2.2
6.0
— 8.8
—12.1
29
—10.9
—12.7
24.2
8.8
17.4
18.5
7.3
2.0
30
6.1
7.2
—26.2
—27.3
—25.6
—27.3
-12.7
—19.0
31
—32.6
—34.5
—17.5
—203
—14.1
—14.5
—13.8
—16.5
32
— 4.6
— 5.1
8.8
7.7
7.2
5.5
— 3.0
-4.3
35
— 6.9
— 8.4
—23.3
-173
—173
—18.0
—11.5
—15.3
37
17.5
21.2
1.0
6.3
1.6
0.7
,28.2
32.2
38
—26.5
—27.2
—17.0
—19.8
-18.1
—19.5
—10.7
—18.1
39
6.6
4.0
—11.0
—13.8
— 2.3
— 7.8
-107
-10.7
41
—11.6
—11.4
—16.8
—19.1
—22.6
-27.5
— 2.1
— 6.1
42
23.1
25.6
— 2.2
-7.5
— 1.7
— 6.0
2.6
3.3
60
— 7.9
— 7.6
34.6
39.2
28.4
31.0
3.0
8.7
81
39.7
33.7
—35.2
-48.1
—53.6
— 4O0
— 70
— 1.3
62
19.8
16.6
—37.8
—39.8
-48.6
—45.5
-21.3
—23.6
54
3.5
4.5
60.7
41.4
32.7
31.1
3.5
16.3
65
—10.0
— 9.2
— 6.0
— 7.6
0.4
1.5
-175
—11.8
57
—25.2
—25.8
-^1.5
— 3O0
—26.3
—25.0
-7.8
—10.4
58
17.4
21.7
4.3
4.9
0.8
1.6
12.9
14.2
59
-4.2
— 4.0
—17.8
—20.1
0.7
2.7
—12.7
—11.8
60
—23.2
—23.9
—12.3
—13.8
—16.3
-24.4
—10.1
—13.0
61
—20.1
—208
— 6.5
1.4
—11.7
—18.5
-3.5
— 1.3
62
42.1
45.6
15.2
16.4
13.7
13.1
3.6
3.6
63
—15.5
—21.0
— 1.3
4.2
9.9
9.5
12.2
5.3
66
101
10.1
—12.8
—16.8
-76
—11.3
—17.3
—14.7
67
09
2.7
27.7
29.7
29.7
29.5
— 8.7
— 8.7
70
—172
—18.3
—21.3
—18.8
-17.3
—13.3
— 1.5
1.8
71
— 2.1
— 3.9
6.8
— 2.1
4,5
6.5
5.7
0.0
72
408
40.6
3.5
1.7
-0.'6
1.5
— 0.7
— 3.0
73
6.5
-6.5
19.1
21.4
13.4
16.7
1.3
1.6
74
-24.4
24.6
-6.5
— 6.3
— 8.8
—12.8
— 9.3
— 7.8
75
—17.8
—21.9
43.0
35.4
26.2
28.7
23.9
30.6
76
3.4
6.6
13.0
22.2
12.7
16.6
— 2.1
— 1.0
78
— 6.5
— 7.2
—17.5
—12.6
—13.8
— 8.8
—11.0
—13.0
80
46.7
502
-2.4
— 01
-9.3
— 2.8
— 0.3
— 2.3
82
— 2.2
— 1.5
13.3
15.7
16.9
18.9
16.5
16.6
83
—13.5
—14.7
— 4.9
— 8.5
-1.9
—10.9
— 6.1
— 4.0
84
— 74
— 8.4
35.2
36.9
36.9
35.6
4.2
9 3
86
—27.2
-29.9
2.2
-2.3
2.4
— 1.3
6.2
2.7
87
—17.7
—15.8
8.2
6.7
14.9
19.0
— 73
— 1.8
88
—20.4
—21.3
—17.0
—13.8
—27.8
—22.0
—10.7
—13.8
90
5.9
5.6
34.2
26.9
23.0
26.0
19.9
26.4
92
— 1.7
— 2.1
—10.8
—12.8
— 6.1
— 8.0
— 9.3
—10 2
93
1.4
=167.3
—10.2
173.8
—173
159.0
-21.6
157.0
—10.8
160.0
— 4.1
147.2
13.2
91.7
13.0
' 2 Dev.2
99.6
Statistical Treatment of Results 25
Ind.
Cancelling S
Copying Addresses
Handwriting
1
2
1
2
1
2
1
3.0
8.5
-0.2
-1.6
-0.3
— 0.4
2
—10.5
— 6.0
2.7
5.0
0.6
0.5
3
—19.2
—19.0
— 3.5
-1.7
0.9
0.2
4
0.5
0.5
— 5.1
— 3.3
— 0.7
— 0.6
7
—22.5
-30.0
-6.3
— 4.1
0.0
0.0
9
15.5
12.0
1.2
3.1
0.9
0.4
10
—11.5
— 9.7
— 4.9
-3.4
— 1.2
— 1.1
11
—13.0
-14.9
1.6
6.3
— 0.8
— 1.2
13
— 1.5
1.0
6.0
8.5
2.7
2.4
li
12.8
IS.O
-2.7
— 2.3
— 0.2
— 0.2
15
23.0
18.0
— 2.4
-0.6
— 2.0
— 2.3
16
2.8
5.8
-0.8
0.2
0.5
0.1
18
— 3.5
— 3.5
2.5
5.3
— 0.6
— 0.5
19
— 2.5
—12.5
-2.4
— 0.5
— 0.2
— 0.4
20
9.3
12.5
2.3
2.8
0.1
— 0.4
21
15.0
12.5
-6.0
-5.3
— 0.7
— 0.2
23
— 6.5
1.5
— 2.4
— 0.2
-0.3
— 0.8
24
31.0
32.8
6.5
10.7
— 0.4
— 0.8
26
13.0
10.5
0.7
2.5
-0.8
— 0.8
27
9.5
-0.5
9.1
9.4
1.2
1.2
2S
— 8.9
— 7.0
— 3.4
— 1.4
0.3
0.3
29
11.0
9.5
6.8
9.0
0.8
0.5
30
— 4.0
— 1.0
5.7
6.8
— 1.8
— 1.4
31
— 2.0
— 2.5
— 2.6
-3.4
-1.7
-0.9
32
9.0
1.5
3.3
3.6
1.7
1.9
35
— 7.5
-5.5
1.0
3.3
0.3
0.6
37
19.5
22.0
1.3
1.8
0.3
0.0
38
—10.5
— 8.5
— 4.2
— 3.9
-1.8
— 1.9
39
15.0
16.0
- 1.3
0.3
— 0.3
-0.7
41
—19.2
—13.5
— 0.9
— 1.1
0.8
0.3
42
—11.2
— 3.5
9.9
, 8.2
1.2
0.0
SO
14.3
21.0
5.5
7.4
1.9
1.4
SI
—22.7
—12.1
2.0
3.4
0.0
— 0.1
S2
—20.5
—21.0
-5.1
-5.5
— 1.3
— 1.3
51
—13.5
-9.5
2.8
3.2
0.5
0.8
55
-11.0
—15.5
-3.6
— 0.8
— 0.9
— 0.4
57
—10.0
— 5.5
-2.4
— 1.9
— 1.4
-1.8
58
6.0
4.3
1.7
3.1
-0.2
— 0.2
59
9.5
11.0
-1.7
— 1.1
0.6
— 0.1
60
—14.0
—12.0
-0.7
-0.8
0.1
— 0.1
61
3.5
4,5
-5.4
-4.2
— 1.5
— 1.7
62
7.3
11.0
3.7
4.5
0.6
0.8
63
3.0
1.5
— 2.5
-3.7
— 1.3
-1.0
66
5.5
6.0
— 4.8
-3.2
0.4
0.5
67
— 2.0
— 3.2
— 1.3
0.0
1.2
1.5
70
—13.0
-11.5
0.1
2.5
0.3
0.3
71
3.5
3.5
1.5
0.0
— 1.2
— 0,8
72
— 9.5
— 5.0
0.7
2.7
0.4
0.1
73
10.5
8.7
— 5.7
-4.0
0.4
0.3
74
5.5
3.0
— 2.0
-1.1
-0.6
0.1
75
26.8
26.5
— 1.0
0.8
1.5
1.3
76
2.0
6.0
10.0
10.0
2.7
2.1
78
—17.5
—10.5
-0.3
0.6
— 1.1
— 1.3
80
0.0
— 4.0
2.1
3.1
1.4
1.1
82
—18.0
-8.9
2.2
4.8
0.7
0.7
83
11.8
12.4
1.2
2.4
0.1
0.7
84
0.0
13.5
0.1
2.7
— 0.4
-0.3
86
3.5
2.5
— 3.7
-36
0.2
0,2
87
— 4.5
0.2
-2.3
— 1.3
— 0.5
-0.3
88
—11.0
— 6.0
— 6,2
— 4.6
— 1.1
— 0.9
90
23.5
29.0
2.1
4.8
0.5
0.7
92
— 3.6
-3.3
2.4
3.1
1.7
1.6
93
— 1.5
-1.6
2.1
3.2
0.8
0.5
\l 2 Dev.» = 99.9 97.6 31.0 33.9 8.36 7.72
26 Correlation of Psychological and Educational Measurements
TABLE D (continued)
Ind.
Visual
Vocabulary
Completion
Arithmetic
1
2
1
2
1
2
1
+ 4.1 + 1.8
00
—12.4
— 1.9
1.4
2
+ 2.1 + 9.6
9
7.6
1.1
1.4
3
— 8.9 + 1.6
— I
— 6.4
1.1
1.4
4
— 3.9
-3.4
— 1
— 6.4
-0.9
— 1.6
7
-13.9
-4.4
1
— 3.4
— 0.9
— 1.6
9
- 7.9 + 1.6
-3
-5.4
2.1
1.4
10
-1.9 -
- 1.4
8
— 4.4
-0.9
— 1.6
11
+ 2.1 + 7.6
— 4
2.6
1.1
0.4
13
-4.9
-7.4
-3
-3.4
1.1
— 0.6
H
+ 3.1 +16.6
-3
— 1.4
0.1
0.4
15
-8.9
-6.4
— 2
0.6
— 1.9
-2.6
16
+ 5.1
-0.4
—11
— 2.4
2.1
— 0.6
18
--5.1 +1.6
— 1
2.6
0.1
— 1.6
19
- - 0.1
-10.4
— 4
-3.4
0.1
0.4
20
-0.9
-1.4
00
1.6
— 0.9
0.4
21
-3.9
-6.4
-3
— 1.4
-1.9
— 1.6
23
+ 1.1 + 4.6
— 5
1.6
1.1
0.4
24
+ 1.1 + 1.6
00
— 0.4
— 0.9
0.4
26
— 3.9 + 1.6
— 2
-0.4
— 0.9
0.4
27
+12.1 + 8.6
13
16.6
1.1
1.4
28
+ 3.1 + 1.6
6
— 4.4
— 1.9
— 0.6
29
+ 3.1 -
-0.4
— 6
1.6
1.1
0.4
30
+ 0.1 + 5.6
— 2
3.6
0.1
-0.6
31
+ 6.1 + 0.6
1
— 1.4
1.1
— 0.6
32
+ 2.1 + 0.6
00
0.6
— 1.9
— 1.6
35
+11.1 +12.6
17
11.6
2.1
-0.6
37
-3.9
-3.4
00
0.6
— 1.9
— 0.8
38
— 2.1 H
h 3.6
00
0.6
2.1
0.4
39
+ 3.1
- 1.6
— 1
0.6
1.1
0.4
41
--8.1
- 6.6
8
6.6
2.1
0.4
42
--2.1
- 3.6
00
3.6
1.1
— 0.6
5C
-3.9
-5.4
— 2
— 2.4
— 0.9
— 2.6
SI
+ 3.1 J
h 6.6
8
2.6
0.1
1.4
52
-1.9
-8.4
— 3
0.6
0.1
0.4
54
—13.9
-4.4
— 2
— 3.4
— 0.9
— 0.6
55
+ 2.1
1-1.6
— 6
— 3.4
1.1
0.4
57
+ 2.1
-2.6
2
-0.4
1.1
-0.8
58
-4.9
-0.4
— 2
— 2.4
0.1
— 0.6
59
+ 3.1
- 1.4
2
4.6
— 0.9
— 0.6
60
-1.9
-10.4
— 5
-9.4
2.1
-1.6
61
+ 1.1
-3.4
— 1
— 1.4
— 1.9
0.4
62
+ 4.1
1-7.6
3
7.6
0.1
0.4
63
-1.9
-6.4
00
0.6
-1.9
— 0.6
66
+ 0.1
-1.4
— 3
— 1.4
— 1.9
— 0.6
67
-2.9
-7.4
-5
— 4.4
-1.9
-0.6
70
— 5.9
-5.4
— 1
-2.4
1.1
— 0.6
71
— 1.9
-0.4
1
0.6
— 0.9
0.4
72
+ 2.1
1- 06
8
2.6
3.1
2.4
73
+ 1.1
-10,4
-8
-9.4
— 0.9
0.4
74
+ 01
-0.4
00
— 4.4
2.1
1.4
75
3 7.9
-2.4
-8
— 9.4
1.1
-0.6
76
+ 2.1
-1.4
00
3.6
— 0.9
0.4
78
--2.1
f 1.6
5
5.6
1.1
1.4
80
- - 5.1
t- 6.6
12
12.6
2.1
1.4
82
— 0.9
-7.4
7
3.6
0.1
— 0.6
83
+ 7.1
f 0.8
6
— 1.4
— 2.9
-0.6
84
- - 5.1
- 1.6
1
3.6
-0.9
0.4
86
-- 0.1
- 4.6
— 5
-1.4
— 1.9
— 0.6
87
— 3.9
-8.4
—11
3.6
— 1.9
1.4
83
+ 2.1
-3.4
-1
-1.4
0.1
1.4
90
-4.9
f3.6
— 8
0.6
— 1.9
0.4
92
+ 4.1
1-6.6
4
6.6
1.1
0.4
93
+ 1.1 -
-0.4
1
-6.4
0.1
1.4
"^ 2 Dev." =39.8
43.9
40.9
11.3
8.68
Ind.
Reading
Omi
1
2
1
1
— 4.2
— 7.6
-26.7
2
4.8
4.4
+38.8
3
-2.2
— 3.6
-9.7
i
1.8
— 4.6
—21.2
7
— 6.2
—15.6
-8.7
9
3.8
—15.6
+ 2.3
10
— 8.2
— 0.6
+ 1.8
11
5.8
5.4
— 3.2
13
— 7.2
— 5.6
—10.2
U
— 4.2
— 8.6
—24.2
15
0.8
— 3.6
—10.2
16
5.8
0.4
—26.2
18
2.8
0.4
+23.3
19
0.8
-3.6
+ 2.8
20
— 4.2
1.4
— 5.7
21
0.8
— 0.6
-34.7
23
— 1.2
5.4
+24.8
24
3.8
2.4
-5.7
26
— 1.2
— 6.6
— 5.2
27
6.8
11.4
+61.8
28
— 0.2
— 4.4
—11.7
29
-2.2
3.4
—27.2
30
0.8
— 0.6
+36.3
31
1.8
— 3.6
-18.2
32
— 0.2
7.4
+27.3
35
5.8
14.4
+64.3
37
1.8
— 5.6
+ 4.8
38
-0.2
5.4
—14.2
39
— 0.2
1.4
+16.3
41
-0.2
9.4
- -29.3
42
0.8
8.4
- -33.8
SO
— 3.2
— 9.6
— 6.7
51
2.8
3.4
+28.3
52
1.8
0.4
— 5.2
54
— 4.2
—12.6
—29.7
55
2.8
5.4
+*S!
57
4.8
9.4
+ 9.S
58
— 1.2
— 1.6
—28.2
59
0.8
1.4
+ 5.3
60
4.8
— 3.6
-18.2
61
0.8
-3.6
—41.2
62
— 0.2
7.4
-^IH
63
— 0.2
— 6.6
—33.7
66
— 0.2
8.4
+14.8
67
— 1.2
— 5.6
—13.7
70
— 2.2
1.4
—12.7
71
0.8
2.4
— 6.2
72
-0.2
2.4
+33.8
73
— 0.2
— 9.6
—14.7
74
1.8
— 0.6
— 7.2
75
— 2.2
1.4
—27.2
76
— 3.2
4.4
—13.7
78
-2.2
3.4
+14.8
80
— 6.2
8.4
+33.8
82
1.8
-3.8
+24.8
83
— 4.-2
0.4
— 4.7
84
1.8
0.4
—10.2
86
2.8
1.4
-14.7
87
— 0.2
34
— 7.7
88
3.8
5.4
+ 1.3
90
—16.2
— 4.6
—28.2
92
-2.2
6.4
+^tl
93
0.8
— 4.6
+ 33
Statistical Treatment of Results 27
Ak6 in
us Proverb months Teacher Rank
2 1 *
-25.9 -2.4 4.7 -10 -«
+28.6 -0.4 2.7 +2 +9
inn _ 1 i .13 4-10
—19.9
—15.9
—15.9
+17
+ s
-10
-34:9 "lie -"€z -29 -30
—11.9 — 1.4 -16.3 +1 —4
—11.9
—22.9
+35.1
—20.9
-12.4
— 0.9
—14.4
+ 1.6
+ 1.6
-18.4
+ 4.1
—10.9
—49.4
— 2.4
4.7
—10
— 0.4
2.7
+ 2
— 1.4
-5.3
+10
— 2.4
2.7
-21
— 2.4
5.7
. —28
— 2.4
0.7
+ 7
— 3.4
12.7
+
— 0.4
2.7
+ *
— 0.4
—14.3
— 6
1.6
-2.3
—29
— 1.4
—16.3
+ 1
0.6
15.7
—20
— 1.4
—13.3
+23
— 1.4
14.7
—25
— 1.4
-6.3
—17
— 3.4
—11.3
—16
0.6
-5.3
+12
— 0.4
— 7.3
+25
— 1.4
31.7
—26
6.6
-11.3
+31
— 1.4
4.7
—30
2.6
37
+17
— 2.4
-0.3
+ 8
— 1.4
1.7
-3
— 0.4
11.7
—11
6.6
13.7
+29
1.6
10.7
+ 9
O.S
-8.3
— 8
— 2.4
— 0.3
+19
6.6
3.7
--30
— 0.4
3.3
--15
0.6
-4.3
—15
— 1.4
—10.3
+21
— 0.4
-O.S
+ 5
— 3.4
12.7
-31
0.6
2.7
-14
— 3.4
— 3.3
+ 3
— 0.4
-15.3
+26
5.6
9.7
-2
— 1.4
16.7
—24
0.6
—13.3
— 1
0.6
11.7
+22
— 2.4
5.7
—19
0.6
3.7
— 7
— 0.4
4.7
-23
0.6
-17.3
+13
— 2.4
—10.3
-5
4.6
0.3
+18
0.6
29.7
—27
— 0.4
— 8.3
+24
— 1.4
7.7
-13
— 0.4
0.7
— 4
— 2.4
—10.3
+16
2.6
— 8.3
+27
6.6
—18.3
+28
— 2.4
4.7
-22
3.6
— 7.3
-12
-3.4
— 2.3
—18
0.6
—133
+20
2.6
— 6.3
+ 6
— 0.4
— 0.3
-9
4.6
-0.3
+11
— 0.4
3.7
+14
-22
—15.4
±114 =1:4 n:? -^25 -20
+ 0.1
—15.4
+18.1
+19.1
—139
+51.6
+11.6
-11.9
+13.6
— 1.4
+ 4.6
+37.1
+36.1
+ 2.6
+16.1
+49.6
— 8.9
-11.9
-27
+ 8
•19
—17
+19
+23
-28
+29
—24
±i
—18
+28
.-10
--6
-- 4
--31
--14
—11
+25
O.'o — 0.4 — o!s +_5 +7
— 31
+ 1
+28.1 -54 — 3-3 +3 —12
tul ^Ti Tl -2 +^3
+30.6 0.6 il'.7 +22 +27
—29
— 8
—25
— 1
—15
+26.1 4:6 0'.3 +18 +28
—14
+21
— 6
—14.4 — 0.4 0.7 — 4 +16
— 1.9 — 2.4 —10.3 +16 +15
+41.1 2.6 — 8.3 +27 +30
+20.6 6.6 -18.3 +28 +24
-21
+ 5.1 3.6 — 7.3 —12 —18
+ 5.1 - 3.4 - 2.3 -18 —23
+ 1.6 0.6 —133 +20 +13
+ 2.1 2.6 - 6.3 +6 +12
—29.9 — 0.4 — 0.3 — 9 — 3
+ 3.6 4.6 — 0.3 +11 +20
Zn.g — 0.4 3.7 +14 +18
■\j SDev.2=28.7 49.5 180.0 164.0 20.7 82.6 144.3 144.3
28 Correlation of Psychological and Educational Measurements
TABLE D (continued)
Ind. School Mark
1
1
—10.0
2
— 1.1
3
— 1.1
4
-13.1
7
—15.1
9
4.9
10
4.9
11
— 7.1
13
-0.1
14
—18.1
15
2.9
1«
-18.1
18
11.9
19
—10.1
20
0.9
21
—17.1
23
10.9
24
19.9
28
— 8.1
27
17.9
28
—14.1
29
2.9
30
0.9
31
— 6.1
32
—15.1
35
11.9
37
1.9
38
3.9
39
0.9
41
19.9
42
5.9
50
— 1.1
51
17.9
52
— 8.9
54
-20.1
55
— 9.1
57
2.9
58
25.9
59
— 2.1
60
—19.1
61
— 1.1
62
12.9
63
— 6.1
66
5.9
67
—13.1
70
1.9
71
1.9
72
12.9
73
-15.1
74
9.9
75
— 5.1
76
1.9
78
10.9
80
16.9
82
16.9
83
—17.1
84
—10.1
86
— 6.1
87
11.9
88
6.9
90
— 4.1
92
7.9
93
— 1.1
' 5 Dev."
= 87.2
ark
Composite
Visual Vocabulary
+Completioii
2
1
2
1
2
— 9.4
-31.3
—46.8
— 8.3
1.6
0.6
80.2
83.2
9.5
18.6
-6.4
—15.4
—40.8
—15.3
0.6
—16.4
—68.3
—96.4
— 9.3
— 4.4
—12.4
—88.3
-115.1
-17.3
-3.4
— 6.4
38.7
—20.8
-13.3
— 1.4
— 8.4
—14.6
—72.1
-6.3
6.6
— 1.4
— 5.3
— 2.5
4.7
3.6
-1.4
1.8
-23.1
-8.3
-10.4
—26.4
—59.2
-66.9
1.7
13.6
3.6
—25.2
—35.3
-8.3
— 8.4
-10.4
—49.4
—45.7
2.7
-11.4
13.6
56.0
37.7
7.7
0.6
—14.4
—28.5
—61.5
-3.3
-14.4
8.6
-23.5
16.8
0.7
— 1.4
—10.4
-91.1
—64.0
-5.3
— 9.4
6.6
32.4
59.5
2.7
— 0.4
14.6
47.8
77.1
0,7
1.6
—16.4
—46.5
—52.5
— 4.3
— 0.4
10.6
183.6
184.3
28.7
21.6
— 5.4
-48.7
—41.9
-1.3
7.6
— 5.4
—10.2
16.2
4.7
-6.4
-3.4
31.3
14.2
3.7
3.6
—11.4
—24.6
—52.2
4.7
1.6
— 2.4
— 0.3
2.9
2.7
0.6
14.6
158.5
127.0
22.7
29.6
0.6
11.4
43.6
-3.3
-3.4
— 3.4
—22.0
2.3
— 1.5
3.6
3.6
33.5
28.1
3.7
0.6
18.6
96.8
113.9
14.7
13.6
— 0.4
73.0
38.0
5.7
3.6
7.6
—19.2
—37.0
-6.3
— 7.4
11.6
78.5
83.1
5.7
14.6
-7.8
-26.1
—19.7
-1.3
—11.4
—13.4
—82,5
—74.2
-27.3
— 6.4
—11.4
—15.2
—22.2
-1.3
— 4.4
8.6
14.3
23.5
1.7
4.6
10.6
9.2
20.1
— 7.3
— 2.4
1.6
— 1.2
-7.2
7.7
0.6
-6.4
—56.9
—108.4
-11.3
—15.4
0.6
-72.1
-30.6
— 0.3
— 4.4
1S.6
84.8
132.6
11.7
10.6
-6.4
—68.5
—80.8
— 1.3
— 6.4
— 0.4
—15.8
— 6.8
-1.3
— 4.4
— 7.4
-65.6
-flO.7
— 7.3
—12.4
8.6
-23.7
-16.2
— 8.3
— 6.4
— 1.4
— 6.2
2.7
— 1.3
0.6
11.6
115.7
95.0
4.7
8.8
—18.4
—72.2
-«4.2
— 8.3
—18.4
— 4.4
9.7
— 5.8
— 4.3
— 0.4
— 7.4
-47.8
-34.8
-17.3
—10.4
— 1.4
— 9.3
33.8
5.7
— 1.4
12.6
41.3
44.5
7.7
6.6
19.6
133.0
160.9
17.7
17.6
18.6
87.6
55.4
2.7
— 0.4
— 4.4
—41.7
-75.4
6.7
8.6
8.6
— 8.6
40.8
8.7
2.6
5.6
—82.0
—13.3
— 1.3
— 0.4
12.6
—42.8
40.5
— 0.3
—19.4
10.6
-6.9
12.0
0.7
— 4.4
— 8.4
-89.8
-12.S
— 4.3
— 4!4
— 0.4
46.2
51.3
10.7
10 6
— 1.4
14.8
-21.6
-6.3
0.8
482.0 U8.0 73.8 74.0
Statistical
Treatment of Results
29
TABLE E
Weights Given to
Each Test
IN Evolving
A
Composite Measuse
Multiple =
the number by which the deviations of the
tests
to the
left were multiplied or divided to
secure the desired weight
ng.
Sq
. root of Sum Dev.'
Divided by 10*
Multiple
Weight
Given
Addition
I
16.73
-
4
=:
4.2
"
2
17.38
-
4
=
4-3
Cancelling 2
I
15.90
-
5
=
3.2
*t
2
15.70
-
5
=
3.1
Cancelling 3
I
15.00
-
5
^
30
((
2
14.72
-
5
z=
2.9
Cancelling A
I
9.17
-
5
=
1.8
tt
2
9.96
-
5
:::
2.0
Cancelling S
I
9.99
-
S
=
2.0
tt
2
9.76
-
S
=
2.0
Copying Addresses
I
3.10 X
1
^
3.1
U H
2
3.39 X
1
^
3-4
Visual Vocabulary
I
3.98 X
1
iz:
4.0
tt tt
2
4.39 X
I
z=
4.4
Completion
I
429 X
3
=
12.9
it
2
409 X
3
r=
12.3
Arithmetic
I
1.13 X
8
=
9.0
tt
2
0.86 X
8
:=
6.9
Reading
I
2.87 X
2
==
5.7
tt
2
4.9s X
2
=
9.9
Omnibus
I
18.00 X
1
^
18.0
"
2
16.4s X
1
=z
16.S
Teacher Rank
I
14-43
-
2
=
7.2
tt
2
14.43
-
2
^
7.2
School Mark
I
8.72 X
1
=:
8.7
it
2
8.03 X
I
=
8.0
* This figure has no special significance.
3. Calculation of Raw Coefficients of Correlation
A coefficient of correlation is a numerical statement of the
proportionality between two series of measures. If the excel-
lence of the scores made by a number of individuals in one test
is exactly proportional to the excellence attained by the same in-
dividuals in another test, the correlation is positive and perfect.
Using r as an abbreviation for correlation : r = -|-i. If the pro-
portionality is exactly inverse, r =r — i. If there is no tendency
to proportionality at all, r ^ o. If there is a tendency to pro-
portionality r is either a positive or negative decimal according
to the direction of the tendency.
The standard method ^ has been used in calculating all the co-
efficients of correlation. This method is expressed by the Pearson
formula :
% X y
' The Bravais-Galton-Pearson method.
30 Correlation of Psychological and Educational Measurements
Referring to Table D the method of calculating the r for, say,
Addition (i) and Cancelling 2 (i) was, viz.: The deviations in
the Addition (i) column were considered x's while the devia-
tions in the other column were y's. The numerator of the for-
mula was obtained by getting an algebraic sum of the products of
every x multiplied by its corresponding y. The figures at the foot
of the two columns being correlated were the denominators of
the formula. Given these, r was easily calculated. By employ-
ing this method the first measure of every test was correlated with
its second measure; some measure of every test was correlated
with some measure of every other test ; in certain instances, every
column of a few tests was correlated with every other column
of certain other tests. These first coefficients are called raw
coefficients.
4. Calculation of Corrected Coefficients of Correlation
Thanks to the excellent work of Spearman, we now know
that these raw coefficients are not true representations of the pro-
portionality between measures or functions. He discovered that
chance inaccuracies in the original scores did not balance them-
selves out but that they always tended to reduce the correlation
toward zero.^ The correlation was said to be "attenuated." The
next step in this study was to correct the raw coefficients for at-
tenuation. There was used for this purpose Spearman's for-
mula:
^(^PlQl) i^Pldi) (^V2<ll) (rP2Q2)
rpq = -^
'^{I'PlP^) in^Qi)
where, if A and B are the facts to be related, /> is a series of exact
measures of A, 5 is a related series of exact measures of B.
rpq is the coefficient of correlation of A and B, obtainable from
the two series p and q, thus being the true coefficient. />! and p^
are two independent series of measures of A. q^ and q,, are two
independent series of measures of B. rp-^q^ is the correlation
when the first measure of A and the first measure of B are
used, rpjgj is the correlation when the first measure of A and
the second measure of B are used and so on for the remaining
' For a criticism of Spearman's assumption see Brown, The Essen-
tials of Mental Measurement.
Statistical Treatment of Results 31
symbols. It is now clear why two measures for each individual
in every test were necessary. Without two measures the raw
coefficient is the best measure obtainable.
The raw intercorrelations among all the tests (except the prac-
tice tests) for which there were double measures, were calculated
for every column with every other column in that group. This
group also included the Composite. These raw coefficients sup-
plied all the necessary data for calculating the true coefficients
from the Spearman formula. Now the practice tests gave much
more reliable measures for each individual; hence, whenever a
practice test was being correlated with any other test just enough
coefficients were calculated to satisfy the shorter correction for-
mula:
VCrpipa) (rguj)
By the use of either of these two formulas the corrected coefficient
or the true correlation was found for every test or function
which was measured twice. The Age of Reaching the Grade,
while really one measure, was treated as though split exactly in
two, rgig2 in the shorter formula thus being considered as -(- i.
This left only one test uncorrected. Table F gives the corrected
coefficients or the true correlations between the tests and the
functions which they measured. A gap in the table means that
the true coefficient is substantially zero. The correction at that
place was impossible either because one of the raw coefficients
turned out zero or because one was a small positive and the other
a small negative. In either of these cases the correction for-
mula fails to work.
The shorter correction formula above is the same as the
longer formula except that two symbols have been omitted from
the numerator. Theoretically, it would have been better to have
retained the omitted and omitted the retained symbols, but, prac-
tically, the difference in correction is insignificant. The longer
formula is to be preferred but the time required often makes its
use prohibitive.
32 Correlation of Psychological and Educational Measurements
■ f I " r ■ ■
• I' I I < ' ■
MUE'V jauO'Gd T "W^-gi ^HOMOCOUdeqoON ^neo
' I' I I r ■ ■
I' ■ r ■ r f r r r 1 1
■ r r I' I r ■ -
'■'■III
O
3 ■ 1 1 1 1 r ■ ■ ■
^ ■ I' I I I I
S
« iSjEinqEDOA lEnsiA SSSS S§§ "SSSR SSSS
b g ■'■11
^ u
H sassajppv Suiytdoo feSSSS SSSS SSSSSS
o .........
2 ssmnaDDEa ssgB ss sssasns
'^ I r r f ■ I f
HI
I f r r r f f
o
■" >-' tHOS to W3 CO '« CO CO ^t CO 1^ ^ cq O ^
r I' r r f ■ I f r
1 1 1' f r r r r
°0!WPV SS2SS52S?3SgSSSS5
I ■ I ■ ■ ■
g^.S.S.SM-n>-s«to"
gsass a S— Ji 8 a 5
!-. di .■•7'.v,.a S-3— S.SrS
4j V u u v.!
«s.^
^ rt ta cB rt o rt'-H o H « B i»« o o
Statistical Treatment of Results 33
5. Reliability Coefficients
The significance of the corrected r's shown in Table F is de-
pendent on their reliability. This reliability is in turn dependent
on the number of subjects used and the amount of correction
that has been applied. The "reliability coefficient" or the raw r
for two separate measures of any one test indicates the amount
of this correction. The corrected r for two tests whose reliability
coefficients are exceedingly small is of doubtful value. Some
of the factors ^ which make for high reliability coefficients are :
that the function tested be narrow; that the time spent in test-
ing be long; that the test material and experimental technique
for the two tests be identical ; and that there be no large variation
in the condition of the subjects. The reliability coefficient for
every test having a double measure is shown in the table of raw
coefficients further on in this book, but for convenience they
are summarized below.
TABLE G
Reliability Coefficients, together with the Total Time Spent on the
Test or Tests Composing either One of the Two Correlated
Measures
Addition, 100 minutes (10 tests) 99
Cancelling 2, 8 minutes (8 tests) 97
Cancelling 3, 8 minutes (8 tests) 96
Cancelling A, 7 minutes (7 tests) 95
Cancelling S, 4 minutes (4 tests) 93
Cop3fing Addresses, 100 minutes (10 tests) 92
Handwriting, 40 minutes (10 tests) 94
Visual Vocabulary, 30 or less minutes (i test) 53
Completion, 30 or less minutes (i test) 59
Arithmetic, 30 or less minutes (i test) 41
Reading, 30 or less minutes (i test) 37
Omnibus, 60 or less minutes (2 tests) 71
School Mark, i semester 83
Teacher Rank 92
Composite 89
The very, very high reliability of the tests from Addition
through Handwriting is due chiefly to the narrowness of the
functions tested, the similarity of the test material and also, in
the case of Copying Addresses and Addition, to the relatively
large amount of time spent on the tests. Intercorrelation among
these tests scarcely needed correction. The reliability of Arith-
1 These factors do not grow out of our data.
34 Correlation of Psychological and Educational Measurements
metic and Reading is unsatisfactory; that of Visual Vocabulary
and Completion leaves something to be desired; all the rest are
satisfactory. The coefficient for Teacher Rank is surprisingly
large, due probably to the close cooperation of the two teachers
in teaching the same children. So, with regard to reliability, the
only corrected coefficients which need to be closely scrutinized
are those with Arithmetic and Reading.
We have spoken of the reliability of the tests as dependent
on the amount of the correction. It is important to know the
reliability of any particular coefficient derived from these tests.
This is dependent on the number of cases or the number of
individuals. P. E. is the measure of this reliability according to
the formula:
where r = actual coefficient of correlation and
n = number of cases included. If the number of cases were
infinite the reliability would be absolute. We have always used
sixty-three cases, hence
.67 (i — r^)
Jr. SL,. =:
^'63
Using this formula we get:
Probable Error of the
Coefficients of Correlation
r
P. E.
.1
.08
.2
.08
■3
.08
■4
.07
•5
.06
.6
•05
■7
.04
.8
•03
.9
.02
IV
CONSIDERATION OF PROBLEMS AND COMPARISON
OF RESULTS WITH THOSE OF OTHER EX-
PERIMENTERS
1. What Are the Intercorrelations among Some Recent
Educational and Vocational Measurements and Cer-
tain Traditional Tests?
The first problem which this study set out to attack has now
been solved. The corrected coefficients given in Table F are
the answer. Since these correlations will be considered in con-
nection with other problems, a detailed discussion at this place
would be tedious. In interpreting the corrected r's the reader
should remember one fact in addition to the cautions given
in the preceding chapter. Handwriting was scored by amount
copied and no attention was given to the quality of the penman-
ship. A large score in this test might mean that the quality of
the writing had been sacrificed. On the other hand, it might
be contended, from a study of the penmanship of men of great
ability, that increased speed and decreased quality both correlate
very highly with mental power. With no evidence to offer, the
author prefers to leave the matter to the opinion of the reader.
2. What Is the Order of Each Test's Correlation with
Mental Ability?
■ Before this problem can be solved we must have some measure
of mental ability. This study proposes three different standards
by which to measure each test.
The first standard includes all the available measures which
are outside our psychological tests. The ideal standard would
be one which properly weighted all the activities in the life of an
individual. A complete standard would take into account not
35
/
36 Correlation of Psychological and Educational Measurements
only how well one does in a psychological test but also what kind
of grade is made in school, what kind of opinion the teachers
have, how well the games of ball are played, the papers sold, the
errands run, etc. Of all these things there are, outside the
psychological tests, just two measures available: Teacher Rank
and School Mark. The value of these two measures as one of
our standards consists in the fact that they represent an at-
tempted weighting of numerous activities, and that they are
measures free from any preconceived opinions of this study. The
corrected r's in Table F for Teacher Rank and Sch o.dLMark
have been averaged for each test, and the positive size of this
average has been taken as that test's correlation with mental
ability.
The second standard used is the correlation of each test with
the Composite. The Composite co mbines th e standard_Just de-
„5£xib£d_mth~4b«— psychologicaL-tests, Possibly the Composite
gives too much weight to the Cancellation tests but, in view of the
later discussions of this book, it is perhaps wiser to err in this
direction. All considered, the writer believes this to be the best
measure of mental ability available for this study.
The third standard by which to determine the value of a test
as a measure of mental ability is the average of thafcrtest's ^arre-
latioj]is_s«th,-alLthfi_X!thei:, tests. But immediately we get into a
difficulty, a difficulty which was minimized in connection with
the use of the Composite as a standard. A glance at Table F
will show that there are at least two distinct groups of tests which
oppose each other: the Cancellation group and the group rep-
resented by the Complex tests. In evolving the Composite meas-
ure, this difficulty was surmounted by arbitrarily giving a rela-
tively small weight to the Cancellation tests. But with the third
standard where equal weight is given to each correlation the Can-
cellation group will exert an important influence. Obviously, it
would not be fair to give as much weight to five Cancellation
tests as to five other separate tests, especially when the Cancella-
tion group measures such a narrow function. If there were just
one such test the matter would not be so serious. If the Can-
cellation tests are good measures of mental ability then the
Complex tests are not. In this dilemma our first standard proves
its worth. Teacher Rank and School Mark, admitted by all
experimenters to have considerable value . as measures of men-
Consideration of Problems 37
tal ability, vote against the Cancellation group. Further, com-
mon sense shows that the other group measures a wider range
of abilities. Moreover, any one test in the Complex group shows
a wider range of positive correlation. Consequently, no test will
be used for the third standard that does not show a distinct
positive correlation with the first standard. This eliminates Age,
Handwriting, and the Cancellation tests.
Using these three standards the order of each test's correla-
tion with mental ability is shown in Table H.
TABLE H
Order of Correlation of Each Test with Mental Ability by Stand-
ards I, 2 AND 3 AND BY AN AVERAGE OF THE ThREE. (Data from
Table F)
Teacher Rank and
School Mark Composite All other tests Average
1. 00 .66 .80
78
75
73
67
61
60
39
27
12
03
06
23
23
.25
Omnibus
•75
Completion
■73
Teacher Rank
School Mark
Reading
.68
Arithmetic
.62
Visual Vocabulary
■44
Copying Addresses
■34
Addition
.23
Handwriting
■02
Cancelling A
.00
Cancelling S
— .10
Cancelling 2
—.28
Cancelling 3
—.28
Age
—■50
.96 .64
.86 .63
■91 -54
•81 ^53
■72 .49
.80 .56
•54 .29
■37 20
.22 .13
.00 — .08
.00 — .09
—.18 —.23
— .18 — .24
—.26 —.19
In studying Table H it is important that the reader remember
that a coefficient of correlation from arrays of averages is not
necessarily the same thing as an average of several coefficients
of correlation. An example of the former are the coefficients
in the column under Composite, while an example of the latter
are the coefficients in the other three columns. But our problem
is not now to discover the absolute coefficient of correlation be-
tween any one test and mental ability; it is to rank the tests
relatively, i.e., which test correlates most closely, which second,
which third, etc. Each of the three standards should give sub-
stantially the same ranking to each test. In fact, the agreement
38 Correlation of Psychological and Educational Measurements
is remarkable. The average of the ranking by the three standards
is practically the same as the ranking by any one of the standards.
This average can be taken as the answer to our problem.
3. How Close Is the Correlation of Each Test with
Mental Ability?
The answer to the above problem depends upon which standard
is accepted as the best measure of mental ability. Omnibus cor-
relates .75 with Standard i, i.oo with Standard 2, and .66 with
Standard 3. Which is the truest coefficient? To trust to an
average of the three, as was done in section 2, would merely
serve to conceal glaring differences. The Composite is better
than Standard i because it includes Standard i along with many
other valuable measures. Standard 3 or the correlation of each
test with all others gives an equal weight to all the measures
composing it, but all three standards agree that all the tests do
not equally measure mental ability. The Composite gives a
weighting which is, at least, roughly correct. Strictly speaking,
the correlation of a test with all other tests taken separately is
a measure of a test's correlational spread rather than an absolute
measure of its closeness of correlation with all these separate
abilities considered together. So far as the question under con-
sideration goes. Standard 3 assumes that, disregarding chance
errors in measurement, any one test is as good a measure of
mental ability as any other and that any one test is as good as
all averaged together. The Composite, on the other hand, con-
siders a sum of properly weighted abilities a better measure of
mental ability than any one of them taken separately. For
these reasons this study considers the Composite the best avail-
able measure for determining the absolute correlation between
any one test and mental ability.
Since we are hopelessly immersed in theory, we may as well
consider the most important objection likely to be offered to the
Composite. It might be said that the Composite causes a test
to show a spuriously high correlation with mental ability because
it is composed of the tests which are to be correlated with it. On
the contrary it might be argued that to eliminate Completion,
say, from the Composite before correlating it with the Composite
would unfairly reduce the correlation, for mental ability means
Consideration of Problems 39
the ability to do Completion as well as the ability to do the
thousand and one other things which enter into complete living.
To strike a true balance between these two contentions would be
difficult ^ if not impossible, consequently the Composite has been
retained in its original form.
Using, then, the Composite as a standard, the closeness of the
correlation of each test with mental ability is shown in column
2 of Table H. This column reveals five interesting facts :
a. Omnibus and Completion correlate perfectly with mental
ability. To be exact, Completion correlates -}--96.
b. Seven of the tests correlate closely with mental ability.
c. The Cancellation tests give a negative correlation with men-
tal ability.
d. The Age of Reaching the Grade also correlates negatively
with mental ability.
e. The coefficients for the tests which measure power are in
every case larger than the coefficients for the tests which measure
speed.
Mv/What Is the Practical Significance of These Facts
^-^ FOR Educational and Vocational Diagnosis and
Guidance ?
Before considering each of the above facts in the light of the
problem just stated it is interesting to consider another question :
just what is the need for measuring mental ability ? The pseudo-
philosopher derives his greatest pleasure from discoursing upon
the negative correlation which exists between the academic and
the real world. In one respect at least this antagonism no longer
exists. The most persistent demand that has come to the psychol-
ogist in the last few years has been, that he develop a means for
measuring that most elusive yet pre-eminently valuable thing
which we call mental ability. And this call comes from school
and factory alike.
The school wants to adjust its training to the individual differ-
ences of the pupils. How can it measure these differences, is the
question asked of the psychologist. The principal wishes to class-
ify a group of children by ability. How measure the ability?
The junior high school wishes to put in one group the supernormal
1 There is a statistical method by which the amount of spurious cor-
relation can be determined.
40 Correlation of Psychological and Educational Measurements
pupils, in another group the normal, and in another the subnor-
mal. How be certain the pupil is not wrongly placed ? Educators
realize that some pupils simply haven't the ability to deal with
mental elements, abstract symbols and the like. Which pupils?
A class for mentally defective children is being formed. Who
should be in the class ? A college in the West is planning to select
its Freshman class on the basis of mental tests. Are the tests
valid measures of mental ability? Experimenters everywhere
wish to form groups of equal ability. By what standard shall
they be called equal? Sociologists wish to discover if unemploy-
ment is the result of mental defectiveness. How gauge the men-
tality? Makers of mental tests desire a standard by which to
measure their own product. What standard is reliable? The
youthful yet virile science of vocational guidance wants to pre-
vent or diminish the present fearful misdirection of energy.
Business is little less clamorous, but no more need be said to
show the very great importance of discovering excellent measures
of general ability as well as tests for special powers. Now let
us return to the significance of the facts reported in the last
section. The first of these was :
(a) The Omnibus and Completion Tests Correlate Perfectly
with Mental Ability
The problem of measuring every single activity of an individual
in order to determine his general mental ability, is, of course,
impossible of solution. So psychology has been trying to find
a few meiasures which epitomize all possible measures. So far
as the writer is informed, the test which has received the most
favorable mention in this connection has been the Ebbinghaus
Mutilated Text. The Completion Test, mentioned above, is a
development by Dr. Trabue of Ebbinghaus' idea. This study
finds ample justification for the high favor accredited the Eb-
binghaus Test and it congratulates Dr. Trabue upon a modification
of it which is likely to prove still more valuable. If we remem-
ber that mental ability means mental ability as measured by our
Composite, the Completion Test correlates with it -j- .96. The
correlation is not exactly perfect but it is very nearly so.
This study is equally pleased to congratulate Dr. Thorndike
upon having compiled and in part devised the Omnibus Test
Consideration of Problems 41
which correlates -|- i-oo with our Composite. The Completion
Test was given for thirty minutes, the Omnibus for sixty minutes.
Does this correlation of -|- i.oo mean that a test has at last been
devised which gives a perfect measure of an intellect by one hour
of testing? It must not be forgotten that the -|- i. 00 is a cor-
rected coefficient. Were the i.oo a raw coefficient and were the
Composite adequate the above question could be given an affirma-
tive answer. The corrected coefficient -(- i.oo means that were
an individual measured enough times with the Omnibus Test to
be certain of an accurate score, then that individual would have as
perfect a measure as if he had been given all the tests compos-
ing the Composite. How many times and how long each time a
person would have to be tested in order to give a perfect ^ meas-
ure of him in any one function is for a future research to deter-
mine. But granting the Composite is not an adequate measure
of mental ability and granting the correction is a little too large,
the fact remains that the Completion Test and Omnibus Test are
very excellent ones. But because of the multiplicity of mental
functions and the variability of theic performances it is wise
to give several types of tests and possibly to secure several
measures for each type. This brings us to the second significant
fact mentioned a few pages back :
(b) Seven of the Tests Correlate Closely with Mental Ability
Since it is wiser to trust to several tests than to one or two,
those interested in educational and vocational diagnosis, gfuid-
ance, and classification as well as vocational selection will want
advice as to what tests this study would recommend. Of the
fourteen measures used, we consider the following to be the
best and most reliable indices df intellect : Omnibus, Completion,
Visual Vocabulary, Teacher Rank, School Mark, Reading and
Arithmetic. The first five tests are the best. An average from
them will give a good measure of an individual's ability, and that
with the expenditure of just two hours in actual testing. The
difficulty of the purely psychological tests could be varied to
suit the ability of the group being tested. It ought not be long
until other tests are devised which can be added to this small
group. It is not too much to hope that the near future will
1 This term is used loosely, for psychology is far from agreement as
to what constitutes a perfect measure.
42 Correlation of Psychological and Educational Measurements
find psychologists able to measure general mental ability very
accuratdy for a group of any size after one day of testing.
Until that time comes we now have tests which will measure in-
tellect roughly at least. And for many purposes such a rough
measure will suffice.
To the five measures recommended in the preceding paragraph
three criticisms suggest themselves. In the first place, Teacher
Rank and School Mark are not always available. Or in cases
where they are available, it is often impossible to use them because
Teacher Rank is not an absolute measurement and because School
Mark varies in meaning even within one school. In the second
place, the psychological tests recommended, measure, primarily,
abstract ability — the ability to handle ideas and symbols rather
than to deal with "things and their mechanisms." All that we
know ^ about the relation between Idea Thinkers and Thing
Thinkers indicates that the man who is good at manipulating
ideas is potentially good in manipulating things. If the mechani-
cal skill desired requires special training this criticism is more
serious. The third criticism is that such tests as these can only
be given to literate people. This is true but it is a fault which
our schools are repairing every day. These three criticisms
merely limit the usefulness of these measures and they emphasize
the fact that even psychological testing requires the exercise of
common sense.
Another result of this study which may prove of practical
value is :
(c) The Age of Reaching the Grade Correlates Negatively with
Mental Ability
Probably every text-book on the psychology of individual dif-
ferences mentions maturity as an important factor in producing
differences in mental ability. But no educational administrator
now believes that mental age always coincides with chronological
age. If he does so believe, he does not dare use it as the sole
basis for the classification of the school children. A very com-
mon complaint among young teachers is that their chronological
age weighs heavier than their mental age with school superin-
tendents. Besides these immediately practical significances, the
1 We greatly need tests of mechanical ability to experimentally test
this statement.
Consideration of Problems 43
influence of age is of keen concern to almost everyone who is
engaged in educational or psychological research. Correlational
psychology, for example, is in constant fear lest its insidious
influence operate to produce spurious correlation. To be brief,
no one would object to this statement: below the age where
senility begins, the tendency is for the older individuals to be
the more able. In so far as the two sixth grades studied here
are typical of all grades, we find an exactly opposite tendency,
which may be summarized, vis.: in any one class the tendency is
for the more mature to be the less able. This is no rank heresy
nor is it an unpredictable mystery. If a pupil is overage for his
group it probably means that he has been retarded, and this in
turn probably means that he started life with an intellectual
capacity which could be expressed as a minus deviation from the
average. So the influence of maturity is not a simple one, or to
speak more exactly, age is no sure criterion of mental ability.
The meaning of age is dependent upon the group in question.
The scope of the negative correlation found in this study needs
to be tested by experiments upon other grades and other groups.
Even more important is the next fact growing out of this re-
search :
(d) The Cancellation Tests Show a Negative Correlation with
Mental Ability
We say above that Cancellation correlates negatively with the
Composite. The zeros after Cancelling A and Cancelling S
(Table H) mean that in those two cases the correction formulas
could not be applied. In addition to the evidence of Table H
the trustworthiness of the negative correlation is further certified
to by the fact that the Cancellation tests correlated negatively with
each of the seven tests which have shown themselves to be good
measures of mental ability. The coefficients are small but dis-
tinct.
It is beyond the scope and data of this research to consider
why, so far as psychology is concerned, there has been such
a chasm between laboratory and life. We suggest that possibly
we have here, in the negative correlation of Cancellation with the
Composite, one element of a complete explanation. The Can-
cellation Test is a not unfair sample of what traditional psychology
44 Correlation of Psychological and Educational Measurements
has been employing in its laboratories. In order that positively
interpreted results from such a psychological test correspond
to results from practical experience, what is would have to coin-
cide with what tends not to be. But a problem of such magnitude
cannot be settled by the relatively meagre data of this study.
The point of main interest for us is that the Cancellation tests
are now in very common use. A Cancellation sheet is about the
first one that enters a newly established laboratory. One college
is trying them out, along with others, as a partial entrance test.
If other researches substantiate this one and experimenters con-
tinue to use it, the test must be interpreted negatively. But even
here the correlation is so low the test is just about valueless for
any positive purposes.
(e) The Correlations with Mental Ability of the Tests which
Measure Accuracy and Speed Are Smaller than the Similar
Correlations of the Tests which Measure Accuracy, Speed,
and Power
Psychological and educational tests are readily divisible into
two main groups: tests which measure accuracy and speed and
those which measure accuracy, speed, and power. The factors,
accuracy, speed, power, are really elements of every psychological
test, hence our division may seem to the reader somewhat arbi-
trary. The division into two groups is due not so much to differ-
ences of elements as to differences of emphasis. The emphasis
in the first group is upon accuracy and speed so let us call the
tests classified there, 'speed tests.' In the second group the em-
phasis is upon accuracy and power, so let us call these tests,
'power tests.'
As stated before, speed tests measure accuracy and speed
primarily. They are usually simple in form and easily within
the ability of the group being tested. Further, all parts of the
test are about equally difficult. The chief characteristic of this
type of test is that its units seldom approach in difficulty to the
maximal ability of the group being tested. The instructions
accompanying these tests, are to work as rapidly as possible with-
out making errors. Our own Addition is an excellent example
of a speed test. Courtis's Arithmetic as usually given is another
example, though with sufficient time his tests could be used in
Consideration of Problems 45
such a way as to make them power tests. Practically all the tests
employed by the older, traditional psychology, such tests for
example as 'Reaction Time,' 'Cancellation,' etc., belong in this
group.
The power tests involve speed, to be sure, but the chief factors
are accuracy and power. By 'power test' we mean one that
contains units sufficiently difficult to discover the maximal ability
of the person or persons being measured. A power test is usually
of a more complex nature than a speed test. The first part is so
easy as to be within the ability of the stupidest member of the
group being measured, while the remaining parts of the test
grow progressively more difficult until the maximal ability of
the brightest individual is measured. Our Trabue Completion
is an excellent example of this type. The Binet Test belongs
in this group also. Mr. Clifford Woody is engaged in making
arithmetic tests '■ of the same nature. In fact most of the recent
educational and psychological tests could be classified here.
Of the tests used in this study. Cancellation, Handwriting, Ad-
dition, and Copying Addresses are speed tests, while Visual
Vocabulary, Completion, Reading, Arithmetic, and Omnibus are
power tests. We have called the Omnibus a power test not
because it is of the same nature as Completion but because it is
complex, because some of its units grow progressively more
difficult, and especially because all the units of the test hover
close to the maximal ability of the group tested.
For the practical purpose of measuring mental ability which
tests offer more promise, those of the speed type or the power
type? The first evidence we have to offer is shown in column 2
of Table I. The coefficients in that column do not recommend
the speed tests. Of the five different kinds of tests used. Copying
Addresses proves itself the best as a measure of mental ability.
But even it is always surpassed in correlation by what we have
termed the 'power tests.' Of course, this comparison, which
has resulted unfavorably for the speed tests, refers only to the
tests used in this research. Copying Addresses, however, prob-
ably ranks considerably above the average speed test in its corre-
lation with mental ability. At least it probably occupies as
^ "Measurements of Some Achievements in Arithmetic," Clifford
Woody, Teachers College, Columbia University, Contributions to Educa-
tion, No. 80.
46 Correlation of Psychological and Educational Measurements
favorable a position with respect to the speed tests as does, say,
Visual Vocabulary with respect to the power tests. In so far as
this is the case, the scope of our comparison extends to tests not
employed in this study.
It is interesting to enquire into the causes for this difference
in correlation between the speed and power tests. We believe
that the emphasis upon power, not as opposed to but as superior
to speed, is one significant element. Much more experimentation
would be required to establish this view, but so far as they go
our results harmonize with such an assumption. Another sig-
nificant element seems to be the complexity of the function tested.
On the whole the power tests do measure more complex functions.
The Omnibus is preeminent in complexity and in correlation with
mental ability. The Cancellation tests are preeminent as to the
narrowness of function they measure and they are last in their
correlation with mental ability. The tests in Table I are ar-
ranged in the order of their correlation with mental ability. An
order for complexity, so far as we can judge complexity by
external appearance, would seem to correspond very closely to
this arrangement by correlation. It is a matter for congratulation
that the more recent mental and educational tests are embodying
these elements of complexity and power. It is a pity the simple
speed tests are not as valuable as the complex power tests, for
they are easier to score. Furthermore, the complex power tests
are not readily usable in long time practice experiments. By
increasing the complexity of the speed tests we may yet make
them valuable measures of mental ability.
In our comparison thus far we have considered only cor-
rected coefficients. The practical measurer of mental ability
must base his conclusions upon raw scores and not upon scores
derived from many more measurements. Hence a practical com-
parison of speed and power tests must be made with raw as well
as corrected coefficients. Table I gives the raw coefficients not
only of each test with every other test, but, what concerns us most,
the raw coefficients of each test with the Composite. Since each
test has two or more coefficients with every other test, Table I
is rather confusing, so for convenience, the reader is referred to
Table J which is an average of the coefficients of each test with
evety other.
Consideration of Problems
47
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48 Correlation of Psychological and Educational Measurements
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Consideration of Problems
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50 Correlation of Psychological and Educational Measurements
Table J permits a comparison of the closeness of raw correla-
tion between each power test and the Composite with that between
each speed test and the Composite. Consulting this table we dis-
cover that Copying Addresses, which is the best of the speed
tests, shows a correlation of -j- .49 with the Composite, while
Omnibus shows a correlation of -[- -So. In every instance, except
in the case of Arithmetic, Copying Addresses gives a lower corre-
lation with mental ability than do the power tests. So the raw
coefficients say as emphatically as the corrected coefficients that
a better idea of mental ability can be gotten by measuring with
Omnibus, Completion, Visual Vocabulary and the like than could
be gotten by running a practice experiment with Copying Ad-
dresses,' Handwriting, Addition, or Cancellation.
The comparison of the speed and power tests is not yet com-
plete. The speed tests as used in this study make available two
important measures: an average of all the daily scores and the
amount of improvement shown by subtracting the first measure
of a test from the last measure. In general, a power test pro-
vides just one measure or else so few measures that improvability
is too small to be of much use. Hence the power test has but
one measure to balance the two obtainable from a practice test.
It is conceivable that improvability with a speed test is a better
intellectual index than a score from a power test. To discover
if this be the case, the improvements made in the practice tests
were correlated with the Composite. The improvement arrays
were calculated in the following manner: the scores made on
the first day by any one individual in Cancelling 2 and Cancelling
3 were combined and subtracted from the sum of the scores made
on next to the last day. In order to get a reliability measure and
to correct for attenuation, a second measure was calculated for
each individual by subtracting the combined scores made on the
second day from the combined scores of the last day. By a similar
procedure a double measure was calculated for Cancelling A, for
Addition, and for Copying Addresses. The absence of any in-
dividual on any one of the four critical days was corrected for
as in Chapter HI, Sec. i. The improvement thus calculated was
correlated with the Composite by the method described in the
early part of this book, the only difference being that in correct-
ing for attenuation the other half of Spearman's formula was
Consideration of Problems 51
used. The raw and corrected Pearson coefficients are given in
Table K.
TABLE K
Correlation of Improvement with Mental Ability (Composite)
Raw Coefficients
Cancellation 2 + 3 (i) with (2) (Reliability) 83
Cancellation 2 -j- 3 (i) with Composite (2) 26
Cancellation 2 + 3 (2) with Composite (i) 13
Cancellation A (i) with (2) (Reliability) 41
Cancellation A ( i ) with Composite (2) — .09
Cancellation A (2) with Composite ( i ) 07
Addition (i) with (2) (Reliability) 80
Addition (i) with Composite (2) 38
Addition (2) with Composite (i) 13
Copying Addresses (i) with (2) (ReliabiHty) 52
Copying Addresses (l) with Composite (2) 10
Copying Addresses (2) with Composite (i) 00
Average Raw Coefficients
Cancellation 2 + 3 with Composite 20
Cancellation A with Composite — .01
Addition with Composite 26
Copying Addresses with Composite 05
Corrected Coefficients
Cancellation 2 + 3 with Composite 21
Cancellation A with Composite
Addition with Composite 26
Copying Addresses with Composite
If we compare the average raw coefficients of correlation in
Table K with the column under Composite in Table J we see
that improvement in the practice tests was, if anything, an even
poorer measure of mental ability than was an average of all
the scores. By the use of averages Copying Addresses did show
a substantial correlation with the Composite, whereas by the use
of an improvement measure, its correlation dropped almost to
zero.
In considering the practical value of tests, other factors than
those discussed should receive at least a passing mention. These
are ease of administration and scoring and the amount of time
required. Further it is just as important to ask what is the dis-
tribution of the time given to the test as it is to ask how much
time is actually spent in testing. Thirty minutes of testing con-
centrated in one period, for example, is usually more convenient
than fifteen minutes distributed over three days.
52 Correlation of Psychological and Educational Measurements
Of all psychological tests the Binet is the best known and the
most perfectly standardized ; yet for general use it will probably
be supplanted by tests which require less skill and less time to
apply. The problem of extending the sphere of psychological
and educational measurement is very largely that of substituting
group for individual testing. The speed tests and power tests
used in this study are all well adapted for group measurement.
They do not materially differ in ease of administration, nor is
there a very great difference in ease of scoring. There is a differ-
ence, however, and this difference favors the speed tests. The
speed and power tests can be compared for time and convenience
by consulting Table G. This table considered in conjunction
with Table J shows that one hundred minutes of Copying Ad-
dresses when distributed over ten days gives a correlation of
-j- .49 with the Composite. Omnibus with only sixty minutes of
continuous testing gives a correlation of -|- .80 with the Com-
posite. In every instance the time spent upon the power tests
was considerably less than that spent upon Copying Addresses.
To sum up the entire discussion, the power tests give a much
higher correlation with mental ability than do the speed tests ;
and this is true whether average score or improvement is used
as the measure of the speed tests. Further, the power tests equal
the speed tests in ease of administration, and they surpass
them in time convenience. Ease of scoring, only, favors the speed
tests, but this superiority is so slight as to be of small conse-
quence.
The issue thus far has been drawn, on the one hand, between
those of our tests which are simple in nature, which measure a
relatively narrow function, which are considerably below the
upper limits of ability, which have units roughly equal and which
were designed and are adapted to measure speed and accuracy;
and, on the other hand, those tests which are relatively complex,
which measure a wider range of functions, which hover close
to the upper limits of ability or else begin easy and grow pro-
gressively more difficult. Thus far we have considered the com-
parative excellence of these two main groups of tests as measures
of mental ability. We can further draw the issue not between
the two types of tests but between the two methods of adminis-
tering any of them. It has been claimed that the amount of
improvement shown by a practice test is a better intellectual index
Consideration of Problems 53
than are "snap-shots" with those tests. The snap-shot test meas-
ures improvement from birth or conception, not to go back fur-
ther, to the time in the life of the individual when the test is
given. The practice test, on the other hand, measures improve-
ment from the first to the last trial at that particular test. This
issue could be settled fairly only by comparing the coefficients
gotten by correlating the score from the first trial with mental
ability and by correlating improvement, found by practice at
that same test, with mental ability. But here our troubles begin.
Those complex, snap-shot tests which show a high correlation
with mental ability cannot conveniently be used in a practice ex-
periment. And since only those which we have called the speed
tests can be readily used for practice purposes the issue is really
the same as that between the speed tests and the power tests, the
speed tests representing the improvement measure and the power
tests representing the snap-shot score. The decision reached in
the preceding discussion favored the power tests.
It is possible, however, to view the speed tests, such as Addi-
tion, Copying Addresses, etc., as snap-shot as well as practice tests,
and thus secure a comparison of the two methods. The first
trial of these tests has not been correlated with mental ability
but improvement has, and the results are shown in Table K.
If the average from all the trials may be considered as at least
a partial representative of the first trial then the coefficients for
the speed tests in Table J under the Composite reveal some inter-
esting inconsistencies. Measured by an average. Copying Ad-
dresses shows the closest correlation with mental ability of all the
practice tests; measured by improvement it shows about the
least correlation. The average correlates a little closer than the
improvement in the cases of Addition and Cancellation of A's,
while improvement has a slight advantage in the case of Can-
cellation of 2 and 3. However we may explain these apparent
inconsistencies by differences of physiological limit, the fact re-
mains that improvement in these tests is a very poor measure
of mental ability, even poorer than an average, and probably no
better than a first trial. In no case does it even approach a snap-
shot score for a power test.
54 Correlation of Psychological and Educational Measurements
5. What Are Some Theoretical Considerations Growing
Out of This Study ?
(a) Is there such a thing as a negative correlation between
desirable functions? Is the law of human nature correlation or
compensation ?
Rightly or wrongly Emerson is usually held responsible for a
philosophic statement of the law of compensation. The law
has been given a more scientific terminology by certain German
psychologists, especially in connection with their attempt to clas-
sify individuals into types. Stated in whatever form, the impli-
cation is that there exists a negative correlation between desirable
traits. From such a doctrine springs the idea that the higher
the ability in dealing with abstract things, the lower it is in dealing
with concrete things; that slow learners are long rememberers;
that the person endowed with beauty is by the justice of Nature
left devoid of brains; in short that Nature always balances a
superiority with an inferiority. In the third volume of his "Edu-
cational Psychology," Professor Thorndike vigorously assails
this doctrine. "It should also be noted that in original nature
the rule is correlation, not compensation." Or again, "It is very,
very hard to find any case of a negative correlation between de-
sirable mental functions. Divergencies toward what we vaguely
call better adaptation to the world in any respect seems to be posi-
tively related to better adaptation in all or nearly all respects.
And this seems especially true of the relations between original
capacities." In the stand taken by Dr. Thorndike, the author
heartily concurs. Hence it is with no small surprise that he finds
himself compelled to appear as a defender of inverse correlation
between desirable mental functions. The only way to avoid
the necessity of advocating a theory so unpopular with recent
psychology is to call the ability to cancel the figures 2 and 3
or the letters A and S, an undesirable mental trait. The ability to
perceive a thing, pick it out from other things, and do something
with it seems so fundamental to all our mental life that we are
scarcely justified in calling such an ability undesirable. Nor can
we, without outraging the best of our common sense, call unde-
sirable the abilities to do the Visual Vocabulary, Completion,
Reading, Arithmetic, and Omnibus tests, or to make good marks
in school and secure the teachers' esteem. And yet between the
Consideration of Problems 55
Cancellation tests and this more complex group we find a negative
correlation.
If the reader will turn back to Table I and count the number
of coefficients of correlation which have been calculated between
the Cancellation group and the complex tests mentioned above,
he will discover that there are 56 such coefficients. Of these 53
are negative and only 3 are positive. Further, of these 3 not one
coefficient is as large a positive as -)--io while there are negative
coefficients of — .35, — .36, — .37 and — .39. The average of the
3 positive r's is -{-.07. The average of the 53 negative r's is
— .21 (P.E. .08). Some of the negative coefficients are small
enough to be due to chance, but it is much easier to believe that
the 3 positive ones are due to chance. In view of the size of the
negative coefficients and the unanimity of results from all the
tests we are forced to conclude that the inverse correlation is
genuine. Nor is this genuineness unsupported by previous ex-
perimenters. Dr. Chapman ('14), "Individual Differences in
Ability and Improvement and Their Correlation," using the same
Cancellation 2 and 3 tests upon twenty-two college students, found
correlations between Cancellation and Mental Multiplication of a
three-place by a three-place number as follows : .00, .03, .16, — .05,
— .13, — .14. These coefficients will average a small negative.
If future results substantiate our findings, what does it mean?
It means that a negative correlation can exist and that many
more may exist than we at present suppose. There are those
who believe that training in one mental function is transferred to
another in proportion to the size of the positive correlation be-
tween the two. If there be anything in such a belief, positive
transfer accompanying a positive correlation may imply ^ a nega-
tive transfer accompanying a negative correlation. Such a state
of affairs existing would mean that to educate a person in one
trait would be to uneducate him in all the traits correlating
negatively with it. It is not impossible to conceive that some
of the more or less trivial traits intensively developed by the
schools correlate negatively with a hundred valuable abilities.
The mere possibility argues for the future development of ex-
perimental education. Our knowledge is very meagre. The
wells which man has digged in the earth are far more numerous
than the borings which psychology has made into the mental life.
1 Such an implication is not necessarily true.
56 Correlation of Psychological and Educational Measurements
Though all these things be possible, we nevertheless believe
with Dr. Thorndike that the law of human nature is correlation
and not compensation. Although correlational psychology is a
new science, it has several thousand coefficients to show for its
labors. Never before, so far as the writer is informed, has a
negative coefficient been so persistently in evidence. If inverse
correlations were numerous, more should have made their ap-
parance by this time. Further, the negative correlations found
in this research may not mean that the functions are intrinsically
inverse. Had a sufficient reward been offered, it may be that
the brighter pupils in the complex tests would have forged ahead
in the Cancellation tests. In a simple test like Cancellation possi-
bly the brighter children lost interest first. Quite conceivably, dif-
ferent abilities have different interest and attention levels. Simple,
routine, relatively easy tasks might be just right to interest the
stupid, while they bored the abler individuals unutterably. Tasks
difficult and complex enough to interest the abler individuals might
be beyond the interest and attention of the stupid. A complete
explanation of the cause would have to explain at the same time
why the average from cancelling figures gave a negative correla-
tion with the Composite while improvement at cancelling figures
shows a slightly positive correlation with the Composite.
(b) What bearing do our results have upon Spearman's Com-
mon Factor?
The reader will remember that just a few pages back we were
so unwary as to become involved in a discussion of the cause
for a negative correlation. Why mental functions correlate in
any way, whether negatively or positively, is one of the most
vital, most difficult, and most disputed problems with which corre-
lational psychology has dealt. One step toward an explanation
has been an attempt to determine the correlational grouping of
mental traits. Here the question asked is : With respect to their
intercorrelations just how do the multitude of mental traits group
themselves, into one system, two systems or many systems?
Concerning this there are three different theories, the "multi-
focal," the "intermediate," and the "unifocal."
Spearman in an article entitled, "General Ability, Its Existence
and Nature," published in Volume V of the British Journal of
Consideration of Problems 57
Psychology, summarizes the "multifocal" theory, viz.: "Accord-
ing to this view, ability in any performance depends upon a
complex of elementary factors ; the correlation between two per-
formances simply measures the degree in which the elementary
factors demanded by the one happen to coincide with, or to be
bound to, those demanded by the other. The elementary factors
include both 'form' and 'content' ; by form is meant the kind of
mental operation, as discrimination, observation, inference, etc.;
while the 'content' denotes the different sorts of data, as color,
shape, number, etc., submitted to such operations."
Between the "multifocal" and "unifocal" theories there are
various intermediate ones which organize mental traits into a
variety of "faculties," "centers," or "levels." Psychologists who
classify the mental life into "types" or "faculties" imply that the
multitude of functions composing any one "faculty" or "type"
show a close correlation with one another while they show a loose
correlation with traits which belong in a different "faculty,"
"type," or "center." Dr. Thorndike seems to believe in correla-
tional "levels" when he writes: "Correlations seem to be closer
within the analytical or abstracting functions than between these
and others. So also within the purely mental associative functions
like adding, completing words, giving opposites or naming objects,
than between one of them and one of the sensori-motor functions.
The sensivities seem to interrelate only loosely; and any one of
them would relate very loosely to the associative or analytical
functions, even when the latter was busied with data from that
sense."^
The "unifocal" theory is represented by Dr. Spearman's famous
"Common Factor." To quote from Spearman himself : "Here,
the view supported is that all performances depend to a certain
degree upon one and the same general common factor, provision-
ally termed 'General Ability.' Correlations are thus produced
between all sorts of performances, the amount of correlation
being simply proportional to the extent that the performances
concerned involve the use of this general common factor, or 'Gen-
eral Ability.' " ^ This criterion proposes not as many centers as
there are "elementary factors," not as many centers as there are
"faculties" or "types," nor even as many centers as there are
1 Educational Psychology, Vol. Ill, p. 37o.
2 British Journal of Psychology, Vol. V, p. 52.
58 Correlation of Psychological and Educational Measurements
"levels" ; rather it proposes just one center. In the same article
Spearman summarizes the importance of this question by saying :
"This sharp divergence between the three current views appears
to be of grave importance. It bars the way to all interpretation
of our laboriously accumulated correlational data. It confuses
all theory as to the intellectual 'make-up' of individuals. And it
paralyzes our practical power of gauging the intelligence of per-
sons, both normal and insane." Following this statement Spear-
man proceeds to give his proof of the existence of the "Common
Factor" and of the inadequacy of all previous conceptions. After
many psychological considerations he decides that the "Common
Factor" is "some common fund of energy." Finally he concludes
with:
"(i) At present, there exists such a great divergence of opinion
about the correlation between different intellectual performances,
as to impede gravely the progress of psychology.
"(2) But closer consideration of all the actual data of the
different authors shows that this divergence is merely due to
gross misinterpretation. In reality, all the facts indicate unani-
mously, that the correlation arises through all the performances,
however different, depending partly on a General Common Fac-
tor."
Do our results support Spearman's contention and justify
his conclusions ? The first evidence we have to offer is the nega-
tive correlation between the Cancellation group and the Complex
tests. Correlation, according to Spearman, is produced by the
General Common Factor and modified by the "specific abilities"
of the traits correlated. To quote again : " . . . every intellectual
performance may be regarded as proceeding from two distinct
factors ; on the one hand, the specific ability or disposition for
that particular performance; and on the other general ability,
due to the common fund of intellective energy." What Spearman
meant by "specific ability" may be gathered from these quotations :
"An 'ear' for melody is known to be particularly specific, that is,
independent of other elementary capacities." And again, "...
their correlations (specific) do not occur in a pure state, but
only superposed upon correlation of a more general character."
The theory of the Common Factor seems to require that all
coefficients of correlation be positive. How two functions can
Consideration of Problems 59
share in a Common Factor and yet show a negative correlation
we are unable to see. Perhaps the Cancellation traits are ostra-
cized from the exclusive society of the Common Factor. Perhaps
in the tug of war the "specific abilities," heading in a negative
direction, outpuUed the Common Factor. The proved skill of
Dr. Spearman could doubtless defend his theory from such a
trivial attack.
In the article already referred to. Dr. Spearman proposes a
remarkably ingenious and important method of treating correla-
tional results. By this method he proved to his satisfaction the
existence of a Common Factor, hence the fate of his theory de-
pends upon the proper working of this method. We purpose to
treat our results by exactly the same method to see whether they
justify a belief in a General Common Factor. In his article
Spearman gave a correlational table which had the general form
of the one given below. (The coefficients are not the same.)
6o Correlation of Psychological and Educational Measurements
aiTcni^iirri'^ OOoOC4CDOU30>0900000
\i'\
f I r 1
-• I' I' ■ I
•rt iiniea «iiDE3x gsssssfes ass
H r r • I
c
I I I I
-4-*
^ S3SS3JPPV auixdoo ggsa»s5 stesss
"■^S+irrV N^.-lOM CQ^NMM
WW
o
Ah
S3n;n33nB0 SSS SSSBSggg
I' I' I' r r
Van!ii33n«3 gfi; SSSSSSSSS
I I I I' I
r r I' I' f
M M bo bo-s <i o«^ V
B a d B.tJ a K>, " "■-
33i3i3 fe o E S ° "
n a B a S3 aS <9^ s g
uuuuai<o>Htnou
Consideration of Problems 6r
Concerning the table of coefficients which Spearman gave, he
wrote : "The most obvious method would be to devise as criterion
some direct function of all the coefficients in the table. We have,
however, chosen a somewhat different course. It seemed desir-
able to retain the power of noting whether the whole table
obeyed the same law or different parts of it behaved differently.
Also we were anxious to simplify the calculations as far as
possible, in order to appeal to a wider circle of readers. For these
reasons, our criterion was based upon singling out from the table
any pair of columns of coefficients. . . . Our criterion consists
simply in the correlation between one column of figures and the
other; it is the correlational coefficient between the two series of
correlational coefficients; clearly this is just as easy to work out
as between any other two series of values. It should be noted
that this correlation between columns is quite independent of the
arrangement in which the table happens to have been drawn
up."
Also Spearman tells us that he threw away the two coefficients
which had no corresponding coefficients in the other column. And
then, a few pages further on, he says : "Such, then, is the statisti-
cal method which we have devised for deciding between the three
rival theories. If the older view of Thorndike, viz., a general
independence of all correlations, holds good, our correlation be-
tween columns of correlational coefficients should average about o.
If his newer view of "levels" or the almost universal belief in
"types" is correct, then the mean correlation between columns
should be a low minus value. If, finally, the true theory is that
of a General Common Factor, the correlation between columns
should be positive and very high."
Since Spearman's method has been applied to average raw
coefficients it is highly desirable that the halves of a test from
which the coefficients were derived measure substantially the
same thing. Otherwise an average of the raw coefficients would
be somewhat misleading. To this end, no test has been used
which did not show a reliability coefficient of -{-.yo. According
to Table G this criterion eliminates Arithmetic and Reading.
Visual Vocabulary and Completion were combined, thus raising
their reliability coefficient to -{-.69, which was accepted as satis-
factory. The intercorrelations of the accepted tests are given
in Table L. It is upon this table that we purpose to test the
62 Correlation of Psychological and Educational Measurements
Spearman theorem. The reliability criterion was set up and the
correlation table was constructed before it ever occurred to the
writer to enquire whether it would operate favorably or un-
favorably to the "Common Factor."
Now, if Spearman's "unifocal" or "Common Factor" theory is
to be corroborated, the correlation between any two columns of
Table L should be, to use his own words, "positive and very
high." To be exact. Spearman says the average of all the corre-
lations should be positive and very high. But Spearman himself
would be the first to say that unless all parts of the table sub-
stantially agree, the use of an average would conceal rather than
reveal the truth. He perceived this when he wrote: "It seemed
desirable to retain the power of noting whether the whole table
obeyed the same law or different parts of it behaved differently."
It cannot be emphasized too strongly that, according to Spear-
man's statistical method, the crucial thing, in the last analysis,
is not the size of the average; it is the size of the correlation
between any two columns taken from the correlational table.
Bearing this in mind, is the correlation between any two columns
of Table L "positive and very high," or does it tend even to be
"positive and very high" ? Taking various pairs of perpendicular
columns from Table L and correlating them we get such results
as the following:
Cancelling 2 with Visual Vocabulary -|- Completion — .gs
Cancelling 3 with Omnibus — .95
Cancelling A with Teacher Rank — .83
Cancelling S with Composite — .91
Any one of the tests shown to the left paired with any one of
the tests at the right would give similar coefficients to the above.
The results are just exactly opposite to what is required to satisfy
Spearman's theory. Instead of the coefficients being "positive and
very high" they are negative and very high. What then led
Spearman to believe in a Common Factor ? The answer is given
in the following :
Cancelling 2 with Cancelling 3 -l-i.oo
Omnibus with Visual Vocabulary -|- Completion -|- -99
Many more such high positives could be given. Mere inspec-
tion of Table L will show that the correlation between any two
columns from Cancelling 2 through Cancelling S would give a high
Consideration of Problems 63
positive. A high positive coefficient would also be gotten from
any pair from Visual Vocabulary -j- Completion through Com-
posite. On the other hand, the correlation of any column in the
first group with any column in the second would be a high nega-
tive. What would the average be ? A mistake !
Lest anyone should think that the coefficients from correlated
columns always approximate unity, note the following smaller
coefficients :
Handwriting with School Mark — .56
Cancelling 2 with Copying Addresses 00
Addition with Visual Vocabulary + Completion -)-.si
Between +.51 and — .56 other intermediate coefficients could
be given. By the proper selection of columns to be correlated,
data could be found to support all of the three main theories, the
"multifocal," the "faculty" or "type" or "level," and the "uni-
focal."
Objections will be urged against our correlational table (Table
L). It could easily be said that Teacher Rank does not measure
a mental trait at all, unless perhaps it be a mental trait of the
teacher, and therefore such a measure should not be included in
the table of correlations. It was retained because Dr. SpearmaH
speaks of using "Imputed Intelligence" in his tables. But the
omission of Teacher Rank would not change the general con-
clusion.
The only really important criticism would concern itself with
the number of the Cancellation tests. Spearman would probably
say that because of them our table is overloaded with "specific
abilities." He himself combined two Cancellation tests which
occurred in one of his tables, though he offered no justification
for such a procedure, except that the tests were similar. If the
tests were practically identical there could be no objection to
his combining them. Likewise it would be difficult to protest
had he elected to treat them separately, for they were not exactly
the same test. If correlation be due to "specific ability" plus
"Common Factor," we should not forget the work of Thorndike
and Woodworth. They have shown experimentally that traits
which seem almost identical may really not be so at all. If
external similarity be our measure of "specific ability," the corre-
lation between Cancelling A and Cancelling S would be higher
64 Correlation of Psychological and Educational Measurements
than between Visual Vocabulary -j- Completion and Omnibus.
As a matter of fact, the correlation is -f--57 in the first case and
-)-.6o in the second. There is no more reason for combining these
two Cancellation tests than for combining the Visual Vocabulary
-|- Completion and Omnibus. But supposing we yield the point
and retain only Cancellation 2 and Cancellation A, then the re-
maining columns can be correlated to give a result like this :
Cancellation 2 with Omnibus — .94
But to be still more generous, we have thrown out every Cancel-
lation test except Cancelling 2 ; yet we can get a result like this :
Cancelling 2 with Omnibus — .92
In view of the foregoing we are forced to conclude that Spear-
man's theory does not have universal validity. And we have
proved this by the application of his own statistical method. Dr.
Spearman certainly bases his theory upon numerous data col-
lected from many sources. His averages certainly were positive
and high, and he explicitly states that no individual correlation
of column with column fell appreciably below positive unity. Had
we correlated every column in Table L with every other column
and had we taken an average of all these correlations, the mean
result would have been a substantial positive. But in view of the
differential action of different parts of the table, such a summa-
tion would be not only misleading but wrong.
Dr. Spearman after advancing and defending his theory of
the Common Factor proceeds to state the nature of it. Concern-
ing the former, Burt writes : "The first of Dr. Spearman's propo-
sitions, the 'Theorem of the Universal Unity of the Intellective
Function' is tested by a corollary logically issuing from it, called
that of the 'Hierarchy of the Specific Intelligences.' Its principle
may be most briefly expressed as follows :
r (A, P) _ r (A, Q)
r (B, P) r (B, Q)
where A, B, P, Q, represent any four capacities not obviously
akin.^ When this formula is satisfied a correlational table can
be so drawn up that the coefficients in horizontal columns grow
1 British Journal of Psychology, Vol. Ill, p. 159.
Consideration of Problems 65
smaller to the right and those in perpendicular columns grow
smaller downward. Burt's coefficients did substantially satisfy
the above formula, and when thrown into the usual table they
formed a beautiful 'hierarchy.' Consequently, Burt agreed with
Spearman's first theorem. The 'Common Factor' and the 'Hier-
archy of the Specific Intelligences' must stand or fall together.
Just as our results do not corroborate Spearman's contention,
neither can our coefficients be so arranged as to show a hierarchy.
Burt, like Spearman, claims that the above formula only holds
when the capacities are "not obviously akin." This is the crucial
point. We are insisting that external similarity is not a satis-
factory measure of kinship. But even when we yielded to ex-
ternal similarity so far as to eliminate every Cancellation test
except one, our results failed to substantiate Spearman's 'Com-
mon Factor' or Burt's 'Hierarchy of the Specific Intelligences.'
Complete fairness to Dr. Spearman makes another remark
necessary. Spearman points out that what he calls "sampling
errors" introduce a definite bias into the results obtained by cor-
relating columns of coefficients, and that to determine the exact
size of the coefficient this bias must be corrected for by a for-
mula which he gives. In order that the correction may not be
so great as to swamp the real difiference, he sets up an arbitrary
correctional standard by which he excludes those columns which
have large sampling errors. Unfortunately, we have been unable
to make clear to ourselves just how he applies this standard,
hence our correlational table has been left unmodified. For this
reason we do not correct our results by his formula but present
them in their raw form. Anyway, the exact size of the coefficient
is not necessary to test Spearman's theory. And even though
Spearman finds that some column used by us did not quite
satisfy his correctional standard, it is hardly conceivable that the
sampling error could be so large as to completely reverse the
direction of the coefficients upon which our conclusion is based.
In correlating two colunms from a correlational table, two
coefficients must be thrown away, one from each column. This is
necessary because there will always be one coefficient in each col-
umn which lacks a corresponding coefficient in the other. But
what is worse still is that every time a new pairing of columns
is made different coefficients are eliminated. This increases enor-
mously the labor of calculating the intercorrelation among the
66 Correlation of Psychological and Educational Measurements
columns, for with each new pairing a new average, a new set of
deviations, and a new sum of deviations squared must be calcu-
lated. In calculating the Pearson coefficients for ordinary arrays
these things are done but once. To minimize labor, therefore,
we suggest that the coefficient -|-i.oo be inserted at every place
in the correlation table where there is a gap. An array will, of
course, always correlate -|-i-00 with itself. This coefficient is
usually omitted in drawing up a correlational table because to
insert it would not be particularly illuminating. Where, however,
we wish to apply Spearman's statistical method such an inser-
tion would prove exceedingly serviceable. We did not use the
-f-i.oo in calculating any of the coefficients used in our attempt"
to refute the two theories of Burt and Spearman. We believe
that to fill up the gaps in a correlational table in this way is
theoretically correct. In every case where we have tried correlat-
ing columns with and without the -)-i.oo the coefficient has been
very nearly the same. But even though the coefficients were not
the same, the insertion of the -\-i.oo might still be justifiable. We
merely mention it here in the hope that some one with sufficient
training in the theory of correlation will test our suggestion.
CONCLUSION
The mere wording of a question may stimulate thinking which
will result in experimental research. It is our only excuse for
asking so many questions and giving a final answer to so few.
Certain conclusions grow out of this study, but the amount of
data in any one research is necessarily so meagre that universal
validity can scarcely be claimed for any of them. But in view
of the limitations of the study, the following seem to us worth
a place in a summary :
1. The corrected correlations among the educational and psy-
chological tests and the functions which they measure contin-
uously vary in size from — .63 to 4~-9^-
2. Meaning by mental ability a Composite of all the measure-
ments, the Omnibus and Completion tests correlate with it -|-i.oo
and +.96, respectively. That is to say, a perfect measure of an
individual by Omnibus or Completion would be a substantially
true index of his mental ability.
3. The seven best measures of mental ability together with
their correlations with the Composite are: Omnibus i.oo, Com-
pletion .96, School Mark .91, Teacher Rank .86, Reading .81,
Visual Vocabulary .80, and Arithmetic .72.
4. Ranked in the order of their correlation with mental ability
the complex educational and vocational tests come first, the rela-
tively complex practice tests second, and the simple practice tests
last.
5. The power tests, or those which measured the upper
threshold of ability, showed a higher correlation with mental
ability than the speed tests or those which measured how rapidly
a relatively easy task could be accurately performed. The power
tests were superior not only as to correlation but also as to time
required and the distribution of that time.
67
68 Correlation of Psychological and Educational Measurements
6. The indications are that for a test to show a close correla-
tion with mental ability it should emphasize power rather than
speed and test a relatively complex function rather than a narrow
mental trait.
7. Improvement at a speed, practice test was on the whole not
so good an intellectual index as an average of the practice scores
and not nearly so good an index as a single score from a complex,
power test.
8. In this particular 6 B school grade chronological age corre-
lated negatively with mental ability.
9. The Cancellation tests correlated negatively not only with
the Composite but also with all those tests which proved to be
good measures of mental ability. This demonstrates that a nega-
tive correlation between apparently desirable traits can exist.
Heretofore, the weight of scientific evidence has been against
such a possibility.
10. The correlation between columns of correlational coeffic-
ients does not corroborate Spearman's important "Theorem of
the Universal Unity of Intellective Function."
11. In no way can a correlation table be so constructed from
our coefficients as to satisfy Burt's "Hierarchy of the Specific
Intelligences."
12. A suggestion was made whereby gaps in a table of co-
efficients can be filled. This suggestion, if justifiable, will greatly
economize labor in applying to a table of coefficients Spearman's
statistical method of correlating columns of correlational co-
efficients.
VI
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Chapman ( 14) . Individual Differences in Ability and Improve-
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Nature. Brit. Jour. Psy., Vol. 5, p. 51.
Hollingworth (13). Correlation of Abilities as Affected by
Practice. Jour. Ed. Psy., Sept., 1913.
Kelley (14). Educational Guidance. Teachers College, Colum-
bia University Contributions to Education, No. 71.
Simpson (12). Correlation of Mental Abilities. Teachers Col-
lege, Columbia University Contributions to Education, No.
S3-
Spearman (04). General Intelligence Objectively Determined
and Measured. Amer. Jour. Psy., Vol. 15, p. 201.
Spearman and Krueger (06). Die Korrelation zwischen ver-
schiedenen geistigen Leistungsfahigkeiten. Zeitschrift fur
Psychologic, Bd. 44, s. 50.
Thorndike and Woodworth (01 ) . The Influence of Improve-
ment in One Mental Function upon the Efficiency of Other
Functions. Psy. Rev., Vol. 8, p. 247.
69
70 Correlation of Psychological and Educational Measurements
Thorndike (09). The Relation pf Accuracy in Sensory Dis-
crimination to General Intelligence. Amer. Jour. Psy., Vol.
20, p. 364.
Thorndike (13). An Introduction to the Theory of Mental and
Social Measurements. Teachers College, Columbia Univer-
sity.
Thorndike (13). Educational Psychology, Vol. III. Teachers
College, Columbia University.
Whipple (10). A Manual of Mental and Physical Tests. Balti-
more, Warwick and York.
WissLER (01). The Correlation of Mental and Physical Tests.
Psy. Rev., Monograph Supplement, No. 16.
Wyatt (13). The Quantitative Investigation of Higher Mental
Processes. Brit. Jour. Psy., Vol. 6, p. 109.
VII
APPENDIX
General Instructions for the Six Preliminary and Six Final Tests :
I am going to give you several tests to find out how good a score
you can make. Do your best in each test. To-morrow I shall read the
names of the two making the highest total scores. Notice carefully all
instructions so you will not need to ask questions and thus disturb others.
(Read before each series.)
Instructions for Visual Vocabulary, Reading, Completion, Arithmetic,
Omnibus and Proverb:
There will be placed before you, face down, a sheet of paper. This
paper tells you what to do and how to do it. You will have 30 minutes
in which to complete the test. When you have finished everything on the
paper, bring it to me and return quietly to your seat. Don't look at
your paper until I say "Go," and stop instantly when I say "Stop." Do
what it says to do.
(Read before each test.) (Proverb: 15 min.)
Instructions for Cancellation :
You will be given a cancellation sheet. In this sheet a certain specified
number or letter must be cancelled. Omit as few cases and cancel as
many as you can in one minute. The sheet will be placed before you
bottom-side lip. When I say "Go," turn the sheet over and commence to
cancel. When I say "Stop," cease immediately. Your score will be as
follows: 2 (number cancelled correctly) minus 2 (number omitted) minus
3 (number wrongly marked). Watch while I show how it should be done
and then you can practice at it yourself for one minute.
Instructions for Addition :
You will be given a sheet containing columns of one-place numbers.
Place it before you bottom-side up. When I say "Go," turn the sheet
over and begin adding. Write the sum of each column of ten figures
under the line at the bottom of that column. Add as many columns as
you can in ten minutes without making errors. If an answer is wrong
you will receive no credit for that column. When you finish the examples
on one sheet take another. Watch while I show you how it is done and
then you can practice it yourself for five minutes.
Instructions for Copying Addresses :
You will be given a sheet containing 25 names and the directory from
which these names were taken. Look in the directory for the first name
71
72 Correlation of Psychological and Educational Measurements
on your sheet, find the New York City address and write it after that
name on your sheet. See how many of these addresses you can correctly
copy on your sheet in ten minutes. Do not begin until I say "Go," and
cease immediately when I say "Stop." Watch while I show you how it
should be done.
Instructions for Handwriting:
There will be placed before you face downward a printed paragraph
which you are to copy as much of as you can in four minutes. You will
be scored for both quality and speed, so write as fast as you can while
writing the best that you can. Be sure to punctuate and capitalize just
as it is in the paragraph before you. Begin when I say "Go," and cease
immediately when I say "Stop." Watch while I show you how to do it.
Teachers College, Columbia University, publishes the Visual Vocabu-
lary, Reading, and Completion tests. Further information concerning
the other tests may be had by communicating with the author.
Appendix 73
TABLE M
Cancelling A: Original scores made in i minute by 88 children.
Ind.
2/4
2/5
2/8
2/9
2/10
2/11
2/15
2/16 2/17
2/18
4/14
4/15
4/16
4/lS
1
18
44
38
48
48
72
58
62
64
60
80
90
78
84
2
32
38-
32
32
48
38
46
56
48
44
48
60
70
3
16
24
30
40
44
54
45
50
68
62
64
48
74
74
4
20
24
40
48
62
54
54
58
80
63
66
58
74
74
5
20
38
40
48
46
60
60
70
64
66
70
—
6
—
—9
~4
4
18
80
45
45
52
60
72
80
76
7
-28
32
36
52
44
66
60
70
66
76
60
48
68
62
8
34
36
38
40
42
48
50
54
60
68
74
69
9
—
58
58
74
74
74
76
88
88
70
92
98
—
10
26
30
30
36
38
48
48
63
44
64
40
44
62
64
11
28
32
40
38
48
54
52
63
63
—
60
69
84
85
12
28
58
58
74
78
78
48
44
90
88
—
—
13
74
44
48
64
66
74
68
68
68
74
74
74
88
92
14
20
36
48
54
64
68
64
62
68
76
62
70
80
46
15
60
54
76
74
96
100
100
92
97
94
92
100
96
100
IS
24
24
48
46
42
62
58
68
72
61
76
68
80
88
17
— 4
22
24
34
30
38
44
34
46
38
28
40
40
40
18
38
38
36
48
60
66
52
64
68
66
60
72
72
62
19
22
36
32
36
42
62
60
62
64
68
64
60
62
64
20
24
28
36
30
34
36
46
54
60
58
52
52
74
68
21
32
34
42
48
50
58
66
48
68
74
60
76
76
68
22
32
28
32
44
42
48
38
56
62
68
50
64
60
23
26
44
50
50
64
62
64
46
62
60
62
44
70
64
24
44
40
52
58
64
68
70
74
84
98
88
96
92
—
25
40
34
50
58
52
74
56
72
61
66
—
—
26
24
38
58
62
72
74
70
76
70
74
74
76
74
27
28
40
28
50
56
60
72
72
76
72
76
88
88
96
28
24
24
26
34
26
38
46
42
62
58
—
40
66
80
29
32
36
36
40
52
82
68
70
78
48
64
68
88
—
30
22
20
28
32
38
40
34
48
44
62
50
64
62
31
26
20
30
32
38
38
38
40
44
44
44
48
50
—
32
28
22
36
40
48
62
52
48
64
64
48
69
80
72
33
32
50
44
52
72
76
72
84
90
80
100
80
100
80
34
36
40
42
48
54
66
—
—
—
—
—
—
—
—
35
16
28
26
34
38
34
38
48
52
44
52
54
64
48
38
16
30
28
30
40
44
38
10
20
62
46
54
70
64
37
40
58
74
76
76
98
84
90
%
100
92
100
102
116
38
22
28
32
44
40
18
38
40
52
44
48
44
60
62
39
40
41
22
38
24
18
38
28
24
32
42
20
50
38
42
60
52
62
68
72
70
44
40
46
58
50
62
54
48
54
68
68
42
10
—
48
34
60
68
62
—
52
64
68
94
92
98
43
38
38
44
44
64
60
76
54
66
70
68
68
76
76
44
36
72
68
60
74
74
—
76
86
70
94
80
94
82
50
14
40
42
50
66
58
62
62
68
66
70
78
86
104
51
34
32
28
40
44
66
62
68
56
24
38
64
66
56
62
10
22
34
30
34
36
24
24
36
38
36
38
44
44
53
28
34
48
40
40
48
60
64
—
—
54
68
62
64
54
54
64
72
60
100
84
72
69
70
60
68
64
70
55
2
30
34
36
44
60
38
42
60
66
42
44
34
66
58
32
44
46
68
62
52
66
72
74
68
74
62
64
57
28
34
40
44
44
60
46
48
48
62
56
46
50
52
58
38
38
62
56
53
68
66
68
80
84
74
88
94
96
59
12
24
28
24
34
38
38
52
54
62
50
56
62
58
60
16
32
24
36
44
48
60
42
68
56
48
48
48
46
61
28
20
40
50
48
52
68
66
64
88
62
42
68
62
24
44
42
42
48
60
60
60
72
80
66
68
80
80
63
28
46
52
48
52
62
74
74
74
66
78
70
94
68
64
34
40
44
40
48
60
40
66
47
54
— .
50
54
58
66
38
42
14
40
32
12
36
48
58
66
68
66
74
60
68
18
28
18
24
20
48
44
46
50
48
44
46
52
56
67
24
28
36
34
26
42
48
44
48
62
62
62
72
66
68
22
32
30
30
—
— .
—
44
52
48
50
52
66
69
20
36
—
48
46
—
34
—
—
—
.
—
70
38
24
38
48
48
64
54
62
54
64
58
60
70
72
71
22
30
48
44
68
65
61
68
68
74
70
48
84
80
72
26
26
34
40
48
48
64
58
64
62
64
66
72
76
73
32
44
38
54
52
54
56
60
68
68
52
68
78
70
74
28
34
38
40
42
54
42
50
54
64
48
46
60
54
74 Correlation of Psychological and Educational Measurements
Cancelling A (continued)
Ind.
75
76
77
78
79
80
81
84
85
90
91
92
93
2/4
2/5
2/8
2/9
2/10
2/11
2/15
2/16
2/17
2/18 •
1/14
4/15
4/16
4/19
32
59
48
72
74
90
94
92
94
96.
90
100
102
102
24
28
34
40
52
64
56
60
64
68
54
62
68
68
34
40
48
42
52
58
64
46
68
68
72
68
74
76
34
30
36
32
40
48
42
46
46
58
46
46
46
46
-39
—58
—46
—42
—56
—45
-54
-68 ■
-93
—67
34
34
36
46
28
20
44
44
41
55
62
62
66
70
62
64
62
66
52
52
68
70
66
92
94
92
98
98
88
78
88
100
52
52
68
70
66
92
94
92
76
66
60
96
92
74
40
SO
40
40
34
48
46
S4
66
76
36
48
42
56
42
66
66
56
ei
ei
70
86
82
82
26
58
—
42
56
48
42
56
50
56
62
58
60
54
64
74
66
64
72
22
44
40
62
60
60
S4
56
62
71
52
56
46
24
28
28
30
40
SO
48
38
48
50
SO
46
S4
58
36
54
30
46
52
68
50
—
—
—
—
40
62
64
70
68
78
68
84
74
84
92
100
100
104
34
36
52
60
56
68
68
60
82
76
64
—
28
34
36
44
44
38
48
46
46
64
62
52
48
40
64
56
64
67
64
64
74
74
—
74
76
84
82
Cancelling S : Original scores made in i minute by 88 children.
Ind. 2/11 2/15 2/16 2/17 2/18 4/14 4/15 4/16 4/19
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
31
32
33
34
35
39
40
41
42
43
44
50
SI
52
63
54
55
56
57
50
58
52
40
70
72
80
92
92
48
48
52
56
58
46
64
58
66
24
30
34
27
36
52
43
64
66
52
54
SO
64
70
64
70
70
72
36
62
66
76
68
84
80
-28
—44
—
—22
20
20
38
26
28
12
30
24
32
36
34
40
64
40
34
36
52
62
63
72
80
70
50
56
54
64
78
96
96
96
80
38
52
44
46
54
52
61
54
62
18
32
28
48
—
46
56
72
64
68
44
70
82
94
—
—
42
56
S2
46
70
66
66
76
76
60
69
76
68
88
86
72
78
86
70
74
72
92
80
80
84
96
96
48
52
48
55
74
62
76
92
85
23
22
48
26
40
42
48
48
42
44
44
S2
60
64
60
60
72
74
34
48
40
62
58
66
58
64
64
46
54
58
71
80
78
84
84
88
48
64
74
80
76
88
76
78
84
58
66
70
80
86
98
83
92
74
46
38
62
60
62
70
72
56
70
80
84
88
84
100
100
96
106
62
64
68
64
78
60
72
74
74
72
76
76
80
80
34
58
44
60
68
88
72
82
74
30
36
42
58
54
—
70
66
66
54
64
68
66
68
72
68
92
94
34
48
52
52
56
70
76
64
76
44
44
52
62
62
70
66
66
70
48
S2
48
56
64
84
70
94
84
46
44
44
40
56
64
72
80
76
40
48
42
50
52
56
S2
70
74
62
-22
— 6
14
32
28
22
38
54
50
68
68
82
90
86
94
92
96
36
44
48
48
46
44
66
72
66
52
60
68
•72
72
84
88
94
96
-12
—
36
42
38
48
38
58
52
92
14
—
—
48
60
88
85
92
39
46
52
66
66
66
70
76
70
44
60
54
60
66
80
72
74
76
48
62
76
72
78
96
100
77
90
34
32
48
50
32
65
45
44
46
32
40
40
40
44
46
52
50
44
48
56
—
—
62
72
68
72
33
35
66
56
28
37
68
68
60
28
48
38
52
52
48
44
58
64
66
62
76
76
94
100
84
84
74
26
44
44
48
58
56
64
62
72
Appendix 75
Ind.
2/11
2/15
2/16
2/17
2/18
4/14
4/15
4/16
4/19
58
40
52
48
70
67
68
74
84
88
59
54
60
64
84
70
72
86
72
94
eo
36
44
SO
44
52
52
52
54
58
61
24
54
62
68
70
68
74
72
62
58
57
66
72
66
78
88
72
84
63
48
44
56
64
62
64
64
90
84
64
42
44
56
60
56
—
70
66
66
65
48
28
42
44
66
44
66
58
62
66
48
62
60
64
68
62
72
84
84
67
44
48
40
62
68
64
76
68
63
68
_
34
44
52
64
70
66
69
26
—
70
36
44
44
M
52
«
60
54
58
71
44
60
50
66
66
66
72
72
86
72
38
48
50
56
56
56
62
52
72
73
62
68
62
76
72
62
76
88
74
52
60
66
70
66
70
72
72
68
75
68
73
74
86
88
90
96
108
108
76
48
54
64
64
72
66
68
74
76
77
46
52
70
66
76
76
70
90
92
78
—
26
30
42
62
50
58
62
68
79
-80
-50
—60
46
50
46
58
62
60
80
60
56
56
66
68
56
57
72
63
81
42
62
60
56
68
72
74
76
76
82
42
44
—
48
58
34
62
52
56
83
52
76
78
88
86
84
52
40
62
56
74
76
88
78
90
85
52
32
68
80
86
52
70
56
48
74
72
70
74
70
87
46
50
58
64
68
52
68
66
—
88
40
38
44
48
60
52
66
68
66
89
60
60
—
—
—
—
90
72
72
82
80
96
100
96
92
102
91
72
78
90
84
88
90
86
92
44
52
60
60
60
70
64
—
93
52
44
52
64
—
64
64
72
68
Cancelling
2:
Original scores made
in one :
minute by 88 children.
Ind.
2/4
1
2/5
2/8
2/9
2/10
2/11
2/15
2/16
1
96
84
92
112
120
122
132
146
2
70
82
84
90
88
74
92
3
62
74
78
92
86
94
98
94
4
58
72
78
86
82
92
88
92
5
78
82
86
84
100
90
6
7
—
62
70
7i
80
94
ii
7i
g
50
62
72
76
—
64
62
9
112
108
118
122
116
118
118
130
10
52
56
60
52
60
70
62
74
11
80
80
80
81
94
89
76
118
12
80
96
100
112
108
112
110
112
13
96
108
90
130
140
140
122
120
14
94
102
112
118
114
112
92
104
15
78
70
90
88
94
114
98
106
16
88
74
96
112
106
126
100
100
17
80
82
76
96
100
100
104
118
18
66
74
78
90
82
88
76
90
19
76
84
78
88
92
88
104
96
20
74
78
82
94
92
88
92
98
21
66
78
94
96
98
104
108
122
22
58
62
64
74
—
94
96
92
23
58
76
80
96
102
100
106
110
24
70
78
92
96
90
100
116
102
25
68
86
104
80
106
92
118
122
26
56
66
76
88
76
88
84
88
27
72
86
80
106
100
100
100
118
28
46
60
68
86
96
98
96
102
29
70
102
88
90
112
53
122
112
30
46
54
54
60
62
76
82
31
32
33
68
76
74
74
80
76
76
82
78
74
80
88
106
106
110
114
88
94
98
120
122
134
132
134
34
66
72
86
88
98
108
—
—
35
36 >
37
40
64
60
64
64
66
68
66
52
56
66
80
94
94
96
100
62
74
84
94
104
104
114
110
76 Correlation of Psychdlogical and Educational Measurements
Cancellling 2 (continued)
Ind.
38
39
40
41
42
43
44
50
51
52
S3
54'
55
SO
57
58
S9
63
64
65
6S
67
70
71
72
73
74
75
76
77
78
79
80
81
83
83
84
85
90
91
2/4
2/5
2/8
2/9
2/10
2/11
2/16
2/16
52
60
60
62
88
88
74
78
62
66
70
78
80
60
88
88
66
88
—
—
82
—
58
78
64
74
88
78
88
82
60
94
92
92
104
—
70
82
74
96
88
98
98
96
84
100
111
104
112
128
124
112
102
122
126
130
126
134
126
144
30
28
48
88
44
92
—
32
50
44
50
54
58
60
52
«e
2
4
4
12
12
28
28
28
138
128
128
130
136
138
148
152
78
74.
92
82
86
92
94
98
74
98
122
118
126
128
18
60
74
60
46
50
84
70
80
92
98
98
100
106
100
48
56
68
74
78
68
78
88
54
58
78
88
82
90
90
90
70
94
100
122
88
84
92
94
84
82
94
100
108
110
118
120
62
80
78
100
92
84
84
g«
62
70
78
88
96
84
96
98
88
100
94
100
98
78
82
100
62
60
70
80
84
78
88
84
102
98
104
118
112
114
128
134
48
68
68
70
—
—
—
78
80
—
90
—
—
—
—
42
70
82
74
70
68
74
82
68
72
100
96
104
100
102
100
62
66
82
88
94
92
100
98
90
98
102
112
106
114
120
126
74
80
78
88
96
98
90
96
110
116
142
124
126
132
132
143
82
96
90
98
98
114
114
122
68
90
96
112
112
114
118
123
68
74
66
74
78
70
82
80
70
92
100
97
96
86
100
118
64
78
80
94
98
102
60
88
94
102
100
116
122
130
76
84
104
100
100
110
96
106
88
96
80
78
88
92
96
90
114
72
108
122
100
110
124
104
134
122
m
94
88
92
98
64
76
106
122
108
84
110
123
66
60
64
66
78
74
68
88
76
114
98
98
76
88
100
74
84
124
110
122
106
142
112
86
—
74
92
96
88
112
112
72
80
86
78
84
90
88
96
38
74
74
—
84
68
90
82
2/17
2/18
4/20
4/21
4/22
4/23
4/28
4/27
160
160
154
170
184
178
176
183
96
98
96
102
106
112
122
122
108
104
114
110
134
138
110
138
100
100
94
88
92
100
106
104
98
106
118
112
122
118
120
134
74
100
92
92
78
110
102
m
92
82
84
102
96
108
118
118
126
128
140
158
166
168
170
183
66
74
84
82
86
88
90
98
116
128
94
130
134
130
114
140
112
122
—
—
162
138
148
142
144
154
160
180
154
168
104
120
126
126
128
122
142
148
134
104
102
98
112
120
134
148
104
118
124
126
132
132
134
118
114
104
96
94
—
92
123
98
98
104
100
92
106
104
128
92
100
98
96
98
88
112
112
96
114
98
120
108
132
122
126
122
130
148
114
118
144
142
128
Ind.
1
2
3
4
5
8
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22 118 118 133 98 90—124 114
23 116 123 104 110 112 122 122 122
24 106 110 114 114 128 106 128 117
Appendix 77
Ind. 2/17 2/18 4/20 4/21 4/22 4/23^ 4/26^ 4/27^
i 1! "? ii iM i 106 102 m
I i 1 I 1 I I I I
I I I I I i ii i i
li « ^ 78 110 104 114 112 122
35 88 88 78 110 104 lU 12 "|
S? "" <-» 102 106 102 — 128 "■«
120 124 88 126 108
SB 96 116 100 96
100 m 102 112 m
!? M ^ 100 88 98 102 102 90
^ i?? 1^2? 2 '^ m IS 130
90 88 96 116 100
100 102 100 104 102 112
K Ts M 'Is" 9 m 100" 9
,*i ,S im 104 102 112 108 112
it I i 1 I i i 1 i
I 11111111
136 144 136 112
s 1 'S 1 Is 'i! It ?. r.
I 'i IS 'i il il 1 a s
§ « I I I '1 a s "
s 1 I .i i » i» iH is
I i ;i 1 ? 1 f I
I I 1 I I -1 li i s
I I I I i I I I i
» !!» !!! S S S « H iS
98 102 108
150 132 160
is "S \n lis lii m m ?4o i5|
1 1 i 1 i i i i
I* ig 1^ - 128 "e 138 126 118,
94
7ft 134 136 - JJ5 JJg i22 126 140
1 » i IM li6 142 122 122 13ft
124 - 136 "i
iJ }i! ^!? li 1« 12? iii 148 148
82 1^ Z 108 102 120 120
^ - li i IS z To T4 I
i Z 1 l?t l^J }2i \f2 lii
11; ^^^6 98 90 m 98 112 112 m
89 ,™ i^i iisn 172 168 178 160 160
I I 1 » i i -1 » 'i
Cancelhng 3: Original scores made in i minute by 88 children.
T J 2/4 2/5 2/8 2/9 2/10 2/11 2/15 2/tft
" z i k ''1 z III It? il
|g 1S§ ISS 1" 5o
I 92 96 - - l^f 1?? ^?? *??
? S 72 i 98 I «! »» "I
I ,?| IM 12! 128 124 126 132 134
78 Correlation of Psychological and Educational Measurements
Ind.
2/4
2/5
2/8
2/9
2/10
2/11
2/15
2/16
10
60
80
78
74
74
104
92
m
11
82
116
108
108
122
110
132
132
12
96
112
132
128
122
140
150
146
13
140
142
126
156
146
160
172
158
14
88
106
118
124
114
118
124
102
15
104
100
118
122
140
138
148
128
16
84
96
120
124
116
—
128
128
17
90
94
100
104
112
m
132
118
18
72
82
86
84
104
106
98
104
19
80
80
78
88
106
128
114
20
100
98
94
106
102
99
122
124
21
78
94
102
110
116
122
126
126
22
74
78
86
98
—
100
108
102
23
82
88
100
118
96
132
132
126
24
106
102
104
108
108
120
128
25
88
112
116
100
108
132
134
142
26
70
84
80
90
90
92
98
96
27
80
84
104
98
88
102
114
116
28
64
76
94
114
118
118
130
124
29
104
126
114
122
124
134
138
138
30
S8
64
—
64
76
90
98
88
31
80
90
92
90
88
96
100
110
32
68
86
104
108
112
126
128
114
33
94
118
138
136
132
142
136
144
34
82
—
108
116
124
122
—
35
62
74
72
82
80
86
94
94
36
58
68
84
96
118
116
81
108
37
76
84
92
108
118
128
132
126
38
66
82
84
78
92
90
86
98
39
80
84
90
92
106
116
114
114
40
87
104
—
—
100
41
74
82
72
72
78
86
i
90
42
82
—
104
96
110
108
43
96
86
94
98
106
114
iii
118
44
104
120
116
126
120
128
144
132
50
116
124
—
132
136
142
140
148
SI
36
88
42
100
96
88
80
54
S2
52
64
56
60
58
70
58
70
S3
26
22
32
18
22
36
40
42
54
152
146
126
—
140
138
150
150
55
70
112
116
102
114
116
126
126
56
—
—
116
128
136
148
138
146
57
92
86
82
82
62
98
74
68
58
70
100
122
110
88
95
124
126
59
72
90
88
104
104
100
118
128
eo
38
62
98
70
98
82
100
102
ei
84
104
126
106
83
94
88
92
62
98
110
116
116
124
132
136
132
63
106
112
126
104
94
114
116
128
64
82
88
92
94
90
100
110
104
65
150
130
124
140
124
102
128
66
68
64
84
74
100
98
104
118
67
128
126
136
128
124
140
136
150
68
—
74
82
82
96
69
88
103
—
96
87
__
100
70
70
92
84
84
94
98
102
71
70
118
118
126
120
122
118
122
72
80
80
94
104
94
104
118
126
73
102
120
122
132
126
136
128
134
74
82
84
92
92
104
90
107
lis
75
136
138
130
138
132
134
140
144
78
92
lie
108
118
120
130
136
152
77
114
136
144
152
132
144
158
164
78
78
108
86
84
82
92
84
112
79
92
102
132
118
130
124
122
110
80
66
80
90
100
104
106
108
122
81
100
78
122
122
122
138
136
136
82
92
122
126
122
116
132
126
83
136
140
104
128
96
105
84
132
128
136
124
136
152
lie
138
85
138
104
—
—
86
136
114
114
116
IM
120
94
110
87
104
158
136
120
122
140
132
128
88
54
70
64
76
76
84
80
88
89
100
102
128
108
112
122
114
90
116
114
124
136
124
132
134
140
91
112
—
116
124
120
124
134
138
92
106
96
100
94
106
124
104
106
93
60
S2
78
96
106
98
112
126
Appendix
Cancelling 3 {continued)
79
Ind.
1
2
3
i
i
10
U
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
31
32
33
34
35
40
41
42
43
44
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
6S
69
70
71
72
73
74
75
76
77
78
79
2/17
2/18
4/20
4/21
4/22
4/23
4/26
4/27
156
112
132
112
124
168
122
128
122
131
174
120
130
114
136
172
100
132
107
140
178
124
138
116
144
182
138
136
114
138
182
132
138
112
140
180
136
144
116
140
108
134
120
118
120
iii
130
122
128
108
144
128
136
124
142
118
150
128
138
132
152
132
ISO
144
154
98
128
152
156
116
ili
164
100
172
118
132
160
118
140
m
116
136
176
116
128
162
176
128
130
140
184
130
118
136
132
136
128
128
136
148
128
140
140
142
146
164
154
132
128
146
118
138
142
144
142
128
124
116
130
122
—
124
128
114
108
114
106
116
126
120
128
112
116
106
98
112
112
108
124
136
136
132
140
144
148
158
148
128
132
134
130
140
138
140
150
110
124
106
138
122
118
108
132
128
134
li2
116
132
155
130
124
132
130
126
132
136
144
136
148
112
140
110
110
120
122
132
118
126
116
116
124
136
138
144
140
134
128
128
96
138
138
136
134
142
136
150
146
108
168
102
148
112
142
110
144
94
146
116
148
122
106
108
100
108
120
122
126
118
128
124
136
132
148
142
158
170
144
152
150
140
144
142
134
142
100
102
112
116
m
128
134
132
104
148
136
132
140
—
138
158
128
102
118
136
98
134
120
130
112
108
130
118
126
122
126
120
124
116
126
126
132
128
106
118
120
146
150
40
70
98
110
98
108
112
108
100
126
118
142
150
40
72
124
128
152
148
68
84
26
110
124
132
162
76
82
30
128
120
138
158
70
74
46
124
126
148
172
96
90
136
124
136
176
104
84
140
120
156
176
90
86
30
140
118
162
128
156
124
172
116
176
122
169
132
146
138
142
138
148
72
124
126
110
116
144
122
122
126
112
150
90
154
88
142
104
162
102
154
116
164
126
112
110
130
132
126
132
100
128
136
104
132
148
122
134
160
116
144
144
128
148
130
114
96
150
124
114
126
150
98
114
134
138
98
120
122
148
100
106
140
142
122
160
102
108
142
152
118
lie
172
112
104
134
150
122
136
172
124
112
142
150
126
142
138
168
108
108
149
162
118
140
132
168
122
104
114
104
120
116
122
116
124
136
128
128
124
136
154
170
114
142
114
136
116
132
122
128
128
132
138
136
136
142
142
142
150
136
122
136
138
122
142
120
146
120
148
106
150
110
148
146
166
158
168
156
152
138
178
108
140
136
190
120
132
196
126
138
134
126
130
144
183
132
148
146
190
132
152
160
200
126
154
122
114
130
126
134
128
142
136
140
162
150
144
150
144
8o Correlation of Psychological and Educational Measurements
Ind. 2/17 2/lS 4/20 4/21 4/22 4/23 4/26 4/27
82
142
132
142
150
144
164
172
158
83
—
132
126
138
118
84
28
84
164
162
162
177
160
182
186
—
85
—
—
26
76
94
104
120
120
86
94
112
122
132
134
110
142
134
87
132
136
126
140
144
146
148
142
88
89
90
104
106
88
116
112
124
124
118
119
138
142
176
176
168
174
1^
91
150
144
132
162
138
138
150
128
92
116
120
108
114
116
112
120
128
93
118
—
116
124
118
128
—
140
Addition: Original scores made in lo minutes by S8 children.
Ind.
2/4
2/5
2/8
2/9
2/10
2/11
2/16
2/16
2/17
2/18
1
64
71
85
80
91
98
96
91
103
117
2
31
42
29
36
48
39
41
51
45
3
63
57
67
60
70
82
77
74
78
84
■4
22
42
34
40
39
45
40
46
36
43
5
20
29
27
26
30
38
32
38
6
—
26
25
30
28
27
36
42
47
7
30
38
34
39
38
39
42
48
35
43
8
23
20
19
24
22
24
27
30
9
29
42
41
50
44
55
60
67
63
60
10
9
9
4
8
4
6
12
6
10
16
11
15
13
18
17
14
20
20
18
12
1
12
13
14
14
17
25
20
21
20
23
26
13
65
71
63
S3
96
98
90
87
99
97
14
63
70
65
73
79
79
72
73
84
86
15
17
28
28
37
28
30
34
32
43
43
16
37
38
40
49
32
46
42
44
49
48
17
14
13
18
16
18
27
23
31
32
31
18
39
46
48
52
52
54
53
68
61
69
19
67
53
62
66
64
63
80
77
86
83
20
38
20
44
46
56
69
47
70
59
70
21
13
22
18
18
23
30
23
27
20
31
22
26
28
32
37
—
34
32
38
40
43
23
36
46
39
48
65
65
56
69
63
69
24
42
45
48
57
54
63
47
60
52
68
25
34
36
41
45
49
61
54
63
50
66
26
38
45
42
24
40
40
46
31
45
53
27
38
42
29
39
62
41
48
50
54
60
28
13
15
18
26
24
26
25
19
18
26
29
30
33
36
28
29
33
39
37
40
32
30
38
48
—
51
53
61
67
56
60
62
31
9
15
13
16
18
20
11
21
15
31
32
27
28
33
40
36
39
28
42
45
54
33
40
52
67
68
65
69
57
67
68
70
34
40
47
48
48
61
66
35
25
31
28
37
42
42
39
38
41
41
36
28
27
20
20
26
22
23
21
25
23
37
45
65
60
67
53
73
73
68
69
70
38
13
23
15
23
21
21.
22
21
25
22
39
33
35
36
43
41
42
45
46
52
57
40
34
33
—
—
45
41
24
31
25
22
30
33
27
30
32
33
42
71
—
63
64
69
71
63
76
43
40
66
62
63
61
65
64
69
83
81
44
24
31
22
29
26
28
30
32
35
41
60
29
34
30
36
27
35
41
37
48
61
51
61
74
78
77
80
85
73
89
87
80
62
61
44
54
69
63
64
69
56
65
67
63
23
27
26
28
27
25
33
28
64
28
38
42
42
46
49
40
65
61
53
55
22
36
33
38
37
38
37
39
45
47
66
—
23
18
15
22
17
22
23
27
27
67
13
16
19
23
18
24
22
27
23
24
58
41
63
54
52
50
58
40
67
69
70
69
25
55
36
31
38
36
37
43
38
35
60
16
20
16
24
12
21
24
25
23
27
61
21
30
20
25
26
32
31
34
28
29
62
62
74
74
76
86
81
83
86
94
94
63
22
21
34
29
28
29
35
23
24
1«
Appendix 8i
Ind.
2/4
2/5
2/8
2/9 2/10
2/11
2/15
2/16
2/17
2/18
M
29
35
32
27
24
25
31
34
S»
42
65
25
31
25
22
29
26
21
27
31
66
39
47
49
48
61
51
51
68
61
68
67
34
35
39
40
36
42
42
50
44
49
57
68
45
54
52
47
—
37
—
63
69
70
27
20
22
25
21
22
26
39
29
29
35
84
71
72
29
46
46
46
52
44
48
41
59
54
66
79
76
80
91
87
88
94
102
103
73
32
29
31
37
37
40
33
36
86
48
74
'75
13
19
13
14
13
13
16
19
26
27
22
18
32
22
17
22
27
30
25
27
76
37
48
45
45
34
49
51
51
49
59
77
78
79
80
81
21
27
22
17
19
31
26
18
27
26
32
35
35
35
40
41
41
48
49
63
39
53
62
67
74
75
67
70
79
83
58
74
«»
86
82
85
92
96
94
102
46
56
64
60
68
73
69
66
64
63
82
29
42
40
42
40
41
45
—
45
51
83
84
30
31
26
35
36
32
39
35
37
43
29
44
36
39
40
39
85
86
87
83
25
21
28
23
22
15
20
20
17
15
15
14
25
25
31
24
21
17
26
19
30
21
30
19
31
23
34
27
36
18
33
27
89
90
91
92
.93
47
21
65
22
71
14
64
26
72
36
68
49
74
48
51
52
49
29
33
39
35
38
33
32
48
43
45
42
43
38
43
43
45
48
48
44
41
47
42
44
45
42
42
39
49
—
Ind.
4/14
4/15
4/16
4/19
4/20
4/23 4/26
4/27
1
2
3
4
5
6
7
8
9
10
11
116
39
77
28
23
34
44
34
56
11
7
119
41
63
29
29
41
48
23
45
11
12
118
45
77
42
34
42
53
32
68
11
11
110
34
80
32
35
49
34
50
21
22
112
35
81
35
23
43
49
35
69
14
29
119
39
75
34
35
54
53
62
71
17
11
115
36
68
49
35
55
45
42
71
9
4
24
131
35
77
40
40
52
58
49
80
14
14
22
12
13
14
15
16
17
18
19
20
21
22
23
24
95
51
27
51
28
64
85
59
28
27
56
51
95
72
29
50
29
61
99
58
26
32
60
60
98
76
24
65
37
69
99
68
27
30
63
63
98
56
25
49
31
70
109
68
26
28
52
98
63
25
59
33
71
90
60
26
24
57
45
108
78
35
52
75
101
74
30
62
66
112
82
36
53
45
79
99
78
31
27
55
60
113
94
35
61
45
77
110
70
28
37
65
57
25
26
27
28
29
30
31
32
33
58
59
32
55
18
46
76
60
62
18
38
44
14
53
72
63
65
22
22
59
21
59
78
68
60
23
47
48
13
31
68
65
73
28
46
60
13
47
68
65
75
23
21
73
12
48
80
57
80
22
46
70
15
47
77
66
78
27
42
66
4
55
78
34
35
36
37
38
39
45
15
68
22
67
43
25
76
19
58
46
26
78
23
65
ii
28
81
21
40
49
31
85
18
63
49
70
28
70
45
23
74
22
67
46
30
81
23
71
40
41
42
43
44
SO
29
54
71
42
33
35
73
81
42
45
48
74
83
41
42
42
87
81
32
39
45
72
79
39
46
48
47
85
39
52
61
93
85
33
46
59
69
89
24
43
82 Correlation of Psychological and Educational Measurements
Addition {continued)
l&d.
51
62
63
54
55
66
67
68
59
60
61
62
63
64
65
66
67
70
71
72
73
74
75
76
77
78
79
83
84
85
86
87
90
91
92
14
4/15
4/16
4/19
4/20
4/23
4/26
4/27
98
104
102
91
92
103
93
106
—
...
„
__
—
—
__
^
28
37
31
41
35
35
53
51
57
51
58
70
63
72
35
35
37
31
42
49
40
48
25
25
27
28
32
30
—
—
20
18
24
25
22
22
30
71
76
82
75
77
89
80
87
51
47
38
43
55
59
56
60
27
29
25
26
29
30
35
24
25
61
26
25
33
31
26
85
9i
93
97
101
110
118
121
30
33
42
26
31
35
25
32
25
35
16
32
35
41
24
27
31
32
57
32
—
29
23
60
57
64
57
66
65
64
74
49
58
52
54
64
59
55
73
57
65
59
54
56
66
72
ii
32
33
31
33
38
31
38
39
48
49
40
48
47
—
51
86
88
81
78
97
100
97
103
40
45
48
45
49
54
47
64
24
23
31
24
31
35
30
42
27
31
31
24
33
36
38
28
59
61
57
43
50
64
61
66
20
23
19
20
17
25
33
32
41
39
38
34
39
39
51
45
87
88
94
80
108
105
103
98
97
102
98
108
120
120
122
61
72
72
64
71
76
68
73
45
45
47
54
54
51
54
56
22
42
34
24
40
42
35
37
41
46
43
37
46
48
44
39
26
30
28
28
45
35
41
16
25
20
17
19
22
23
20
33
32
32
25
35
31
44
27
31
31
33
38
39
34
31
62
62
73
69
68
56
73
93
38
49
. —
42
53
52
58
44
54
58
—
47
50
51
58
38
43
52
45
61
65
56
CoFX-iNG Addresses: Original scores made in lo minutes by 88 chil-
dren.
Ind.
2/19
2/23
2/24
2/25
2/26
3/1
3/2
3/3
3/4
3/5
1
7
10
19
18
18
16
17
17
19
15
2
15
19
13
21
22
21
18
22
26
3
3
9
10
17
14
16
16
17
18
18
4
10
10
14
17
13
15
13
11
14
15
5
16
18
19
24
22
23
21
22
24
6
3
7
7
9
11
11
16
—
6
11
7
1
8
5
11
13
15
8
12
14
20
8
13
14
17
20
20
20
15
20
23
25
9
13
19
17
21
18
20
14
16
22
26
10
9
11
10
12
16
12
10
19
12
17
11
5
11
14
—
22
22
17
25
25
28
12
5
11
16
IS
14
10
16
12
19
13
15
21
25
23
20
25
22
26
25
29
14
12
12
9
14
14
13
18
17
13
15
15
9
8
9
IS
16
16
15
17
13
24
16
n
10
15
16
19
IS
17
21
19
24
17
13
12
11
17
17
19
9
15
16
18
18
13
14
14
24
22
25
19
19
23
28
19
5
13
11
16
13
18
15
16
18
23
20
11
16
33
19
20
17
20
17
20
28
21
9
12
9
12
12
15
15
13
8
12
22
11
5
12
17
16
14
18
15
15
24
23
11
12
8
— .
14
21
16
17
13
22
24
17
19
19
24
24
23
20
23
25
25
25
15
15
17
18
23
18
19
21
17
24
28
12
13
17
20
18
21
18
19
18
20
27
IS
17
20
25
25
26
26
29
31
29
28
9
11
10
14
14
13
16
18
13
19
29
15
20
20
27
22
21
26
24
26
29
Appendix 83
Ind. 2/19 2/23 2/24 2/25 2/26 3/1 3/2 3/3 3/4 3/5
30 17 20 25 23 25 21 ?2 23 24 28
31 10 13 - 1* " ii H « m 29
32 14 17 18 20 21 12 JS ?t ?! ?S
33 78 13 14 1913131315W
35 H 16 15 18 ?9 1? " 1? ?» ?i
3« 10 14 9 13 14 19 18 17 18 W
37 13 18 21 21 21 21 13 15 21 28
38 11 11 10 14 15 14 15 14 17 17
12
l6 14 19 18 17 18 14 17 23
40
41 14 11 17 18
20 20 21
42 19 21 25 25 23 26 29 21 SO 29
43 12 5 12 1? 20 11 17 19 16 20
44 11
50 15
51 12
52 2
__ 17 - 16 10 15 16 20
sn l^i 20 18 23 25 — 19 26 24 30
ll ll 18 19 19 24 19 16 20 25 24
_ „ 14 14 12 11 11 13 15
53 - 15 16 18 19 19 18 22 23 27
M 10 13 21 21 23 19 27 23 21 27
55 6 12 12 16 16 20 20 16 16 23
?R 6 13 17 17 19 20 16 24 24 25
52 1? 12 17 14 15 16 15 13 19 19
si 13 ii 15 17 16 1? 16 20 20 20
^^ W \l }? II \l \l 1^" 5J ?J
11 10 12 16 11 12
ll 1 \\ \l Ji 11 1? 11 n II To
*62 1 ?3 23 }? ?2 ?X ?t g
M A 11 13 12 17 15 14 10 18 21
M 13 18 22 I9 24 22 22 22 22 23
«B Q 8 7 — 9 15 14 5 9 la
m 10 5 8 11 15 16 10 16 15 18
H 1? 12 12 15 19 20 17 19 14 21
JI 1161316^181819-24
?n 12 14 14 18 19 23 15 20 23 1?
?? 10 11 14 14 18 18 15 19 16 25
72 12 17 20 21 18 17 19 22 18 24
li 10 10 5 13 13 14 12 12 10 16
ll 8 u 13 17 19 16 18 15 14 21
It 5 7 9 U 19 17 10 19 16 20
™ 21 19 23 27 26 24 29 28 31 31
A ll 18 20 22 21 23 22 21 24 24
i 1? iJ 1^ ^ li " " I
i i i ^ ia i? M I g I
i ^ 1 f? i ?i ^ i I9 I9 I
I 1 II 11 18 18 ^ 18 10 10 ?f
If TT "a X 9 15 19 12 17 10 20
i 1 -8 i i li 1? !? 1^ It ?
S « i» ll 16 19 22 17 21 19 27
90 13 18 IS JO " 10 IS 22 25
,, ?7 « 20 18 18 19 18 22 25
92 8 U 22 2! 2I 19 22 20 25
^ 12 16 19 18 - - 19 26 21 25
Ind. 4/14 4/15 4/16 14/9 4/20 4/21 4/22 4/23 4/26 4/27
21 21 19 24 26 "
26282825252826 30
1 ic 9ft 21 21 21 19 24 26 22 21
i M 28 28 25 25 28 26 30 30 32
18 i 19 20 21 1? 23 22 21
4 18 19 14 18
18 20 15 16 18 25
22 24 28 25 24 26
5 }? « ?2 13 16 18 15 16 18 19
S ]i \l 17 21 21 16 15 20 22 22
I J2 M 27 26 28 28 32 32 34 39
I 2I Is 25 i S 20 28 29 21 29
-^ tn 01 i« 18 18 15 16 18 ^ **
1; II U § M 26 31 31 34 25 ^^
ll w 29 24 32 31 31 31 34 38 34
\l 23 19 21 23 21 « 15 23 25 21
li m M 22 20 21 21 22 25 26 25
IS ?J if io 16 25 22 23 24 24 29
84 Correlation of Psychological and Educational Measurements
Copying Addresses (continued)
Ind.
4/14
4/15
4/16
14/9
4/20
4/21
4/22
4/23
4/28
4/27
17
19
17
19
17
19
20
19
—
24
22
18
26
27
25
26
22
26
28
31
31
.32
19
21
20
13
18
21
22
24
21
28
27
20
23
22
26
27
24
28
31
26
33
.29
21
18
16
17
14
18
17
16
17
16
18
22
24
24
18
18
21
16
22
28
27
23
21
23
20
19
21
22
25
26
25
25
24
25
26
30
27
29
29
32
34
36
36
38
20
26
24
24
2i
24
27
29
28
28
27
29
27
35
32
32
36
37
37
39
35
23
18
19
-24
21
21
19
28
25
19
29
27
30
29
22
30
36
37
31
34
39
30
24
26
30
26
29
27
27
31
32
32
31
18
19
20
15
20
19
19
26
24
22
32
30
28
26
18
24
27
27
28
33
31
33
34
35
17
20
19
10
20
19
21
21
22
17
22
26
M
27
20
25
26
29
31
28
36
19
18
15
14
20
21
23
—
24
24
37
25
23
23
23
24
24
25
23
26
21
38
16
15
15
U
19
19
18
20
20
.22
39
40
41
17
23
21
20
22
22
20
22
26
2S
20
20
19
17
20
23
22
21
24
.18
42
31
29
32
30
33
34
37
34
38
32
43
14
17
18
15
21
17
21
24
24
21
44
20
22
20
20
23
22
23
23
26
27
50
33
28
34
26
33
32
26
30
34
34
51
98
26
28
22
22
29
23
26
27
30
52
68
16
18
17
21
18
21
20
22
19
53
28
29
25
26
24
23
34
—
31
54
63
51
21
22
24
26
28
29
28
31
55
35
35
18
18
21
21
14
20
18
24
66
26
26
25
23
23
27
32
30
57
20
18
19
14
20
21
20
22
20
27
68
71
76
23
28
24
26
30
29
36
31
59
51
47
17
15
23
15
26
26
23
26
60
27
29
21
18
23
20
21
23
22
21
61
25
14
14
15
16
18
18
17
17
62
85
98
18
28
28
31
30
26
29
28
63
30
33
18
19
21
18
25
18
23
21
64
25
25
25
25
23
28
28
29
65
27
31
17
13
16
—
—
19
17
66
60
57
19
20
21
18
19
20
21
24
67
49
68
19
19
18
20
24
26
30
24
68
69
70
57
61
24
23
20
21
23
26
24
27
31
32
25
23
26
26
24
27
21
30
71
39
48
17
25
26
20
26
21
23
72
86
88
21
21
21
26
24
26
29
27
73
40
45
18
14
18
18
21
18
19
22
74
24
23
21
18
21
19
24
22
21
23
75
27
31
26
23
22
22
28
30
31
28
76
69
61
29
28
32
38
34
35
36
36
77
20
23
24
23
26
26
26
27
29
23
78
41
29
21
19
23
22
24
28
26
30
79
87
88
27
23
23
26
21
27
26
80
93
97
23
19
28
26
28
32
32
31
81
61
72
30
36
36
40
37
38
40
38
82
45
45
27
27
25
30
24
29
29
30
83
22
42
26
21
19
24
31
31
30
30
84
41
46
19
22
25
26
29
32
24
28
85
26
30
—
16
16
22
18
23
20
22
86
16
25
16
11
21
19
26
23
22
18
87
33
32
20
—
17
14
23
23
22
25
88
27
31
16
16
14
17
16
19
21
14
89
—
—
—
—
—
90
62
62
23
25
23
34
29
31
31
^
91
38
49
22
25
26
24
24
25
92
44
54
24
25
26
28
26
25
26
93
38
43
27
22
26
23
26
27
28
Appendix 85
Handwriting : Original scores made in 4 minutes by 88 children.
Ind.
2/19
2/23
2/24
2/25
2/26
1
63
70
62
56
63
59
73
71
67
75
2
87
80
80
82
72
72
92
85
85
72
3
83
81
78
71
77
66
72
68
75
79
i
68
62
68
62
67
64
57
60
51
59
S
76
81
79
65
66
72
85
67
69
73
6
80
75
70
66
60
55
60
61
65
58
7
65
64
79
78
78
72
63
67
65
68
8
66
61
55
47
33
38
40
39
51
52
9
85
81
62
68
68
67
66
65
69
73
10
58
57
61
49
46
47
44
72
55
63
11
81
81
60
64
64
51
53
64
44
55
12
80
80
68
SO
—
—
86
85
100
85
13
107
95
81
68
85
64
101
94
83
107
14
67
79
65
58
61
66
77
80
69
63
15
54
59
46
39
45
45
46
45
42
50
1«
86
82
65
65
77
77
72
75
71
71
17
55
55
49
48
48
46
55
54
46
60
IS
63
60
70
70
69
65
64
65
63
59
19
64
65
61
55
55
59
62
65
67
66
20
70
79
67
59
64
63
69
75
57
73
21
55
70
65
66
54
59
61
65
57
68
22
75
67
75
68
73
70
73
88
72
88
23
71
87
60
53
54
60
57
67
55
73
24
68
75
72
58
65
60
58
66
56
72
25
65
68
52
53
59
50
77
60
60
64
26
64
59
59
53
64
58
60
70
61
72
27
78
79
72
76
83
74
80
87
82
78
28
75
79
74
72
66
63
62
65
64
80
29
75
81
84
73
64
64
71
75
68
78
30
55
61
63
55
51
48
—
—
49
55
31
75
79
75
54
—
—
56
49
41
67
32
83
90
97
87
86
85
71
93
71
84
33
81
90
82
68
68
65
78
70
67
59
34
—
_^
—
— -
—
35
70
61
70
61
72
68
74
78
76
74
36
101
89
75
69
73
72
65
69
75
72
37
78
96
70
63
73
61
70
72
54
61
38
51
46
54
43
50
48
51
48
62
50
39
68
74
58
56
53
57
53
66
68
71
40
41
83
81
81
75
57
42
75
83
89
95
42
101
86
79
76
75
71
78
86
88
88
43
73
81
68
60
69
73
67
75
71
79
44
69
75
—
—
—
—
—
—
—
50
92
86
92
68
88
75
95
97
89
96
51
79
75
84
76
77
71
83
67
61
78
52
60
54
51
52
59
60
54
65
53
85
61
76
60
67
84
61
75
54
85
78
78
84
71
66
75
71
65
85
55
69
51
76
77
50
60
67
75
60
69
56
95
89
90
76
94
84
93
102
98
105
57
69
67
60
59
60
48
46
47
45
60
58
71
65
65
65
58
66
69
70
67
70
59
69
65
75
67
74
75
64
67
86
82
60
80
78
66
63
60
66
82
67
72
80
61
45
55
51
41
49
52
53
53
54
60
62
91
74
74
68
68
67
75
89
70
71
63
54
54
61
54
59
58
62
65
61
65
64
78
74
75
63
57
64
71
78
74
75
65
91
85
78
69
82
68
—
70
81
66
81
72
79
74
60
64
76
80
75
83
67
99
96
96
94
75
84
83
90
74
85
68
82
75
82
79
80
70
75
93
66
88
69
70
66
67
70
64
73
59
79
76
72
81
71
66
68
67
64
56
58
68
69
48
63
72
75
75
64
66
70
66
73
83
66
80
73
84
79
75
68
74
72
72
80
69
65
74
74
74
69
85
53
46
73
81
72
69
75
86
79
78
66
80
72
76
95
80
91
76
98
104
89
92
87
82
74
93
101
106
77
72
66
70
60
72
73
64
75
64
68
78
66
65
56
52
54
51
48
60
61
60
79
84
83
75
82
68
77
78
79
75
76
80
95
93
79
62
68
70
88
93
90
86
81
99
100
98
92
95
96
104
100
90
91
82
80
73
84
76
78
75
83
79
79
80
83
71
62
71
60
68
82
65
75
84
83
i2
78
72
71
69
61
80
63
56
86 Correlation of Psychological and Educational Measurements
Handwriting (continued)
Ind.
2/19
2/23
2/24
I
2/25
2/1
»
85
__
69
67
86
86
85
72
76
73
61
70
72
65
72
87
73
78
76
80
76
64
42
70
60
67
88
89
90
58
64
65
48
56
51
64
54
59
70
70
ii
il
76
84
75
63
57
E
89
91
91
89
75
73
64
66
86
83
74
79
92
84
80
75
76
78
78
85
79
89
89
93
79
71
78
63
79
72
75
80
~
~
Ind.
3/1
3/2
3/3
3/4
3/5
1
69
63
59
64
66
54
61
57
69
69
2
63
66
63
67
74
65
57
65
3
67
62
72
77
62
66
73
77
72
81
i
64
61
59
66
61
60
56
65
59
63
5
66
76
69
70
68
64
73
74
6
69
59
64
62
61
45
66
53
7
59
68
63
66
65
71
69
66
66
63
8
44
61
35
41
48
36
44
36
32
46
9
81
71
73
85
74
75
76
81
75
80
10
40
43
53
62
69
63
65
59
67
77
11
46
56
66
66
65
63
45
54
60
62
12
68
75
64
86
75
79
76
86
83
96
13
82
83
104
102
89
107
105
91
101
113
U
64
62
61
61
62
61
69
66
63
69
IS
42
46
46
47
49
61
38
40
39
48
16
66
64
66
60
68
66
67
71
68
79
17
42
50
61
51
48
47
48
51
45
60
IS
61
63
60
66
58
69
63
61
68
66
19
66
76
61
75
64
68
71
68
62
64
20
65
64
64
76
69
70
61
69
67
60
21
59
69
64
64
66
73
66
60
65
68
22
73
70
62
77
68
77
65
50
70
72
23
51
61
63
61
69
67
67
70
66
58
24
47
63
66
70
53
60
55
54
52
66
25
68
61
59
67
58
67
63
63
64
76
26
58
63
54
58
62
63
51
44
56
68
27
81
85
79
93
75
78
63
81
83
80
28
75
75
62
64
62
77
81
68
73
72
29
68
61
53
100
69
60
62
84
68
101
30
34
61
41
48
62
50
46
42
61
64
31
63
56
69
77
45
71
50
38
49
79
32
78
92
86
83
95
88
90
84
81
90
33
67
69
57
76
62
51
47
51
56
82
34
3S
76
74
72
78
77
90
68
59
87
69
36
81
78
70
86
77
78
82
74
85
79
37
55
62
64
80
61
66
64
72
73
87
38
49
46
48
50
49
44
51
46
64
57
39
69
71
57
70
55
69
61
56
66
64
40
—
—
—
—
—
41
74
75
78
78
62
67
75
69
55
60
42
65
57
67
84
45
55
66
68
62
76
43
72
79
40
30
41
65
76
71
68
76
44
70
68
71
76
76
76
74
69
62
69
50
72
89
79
87
81
95
74
93
65
69
61
66
62
62
70
46
69
43
64
62
70
52
65
57
66
66
65
60
50
46
47
52
S3
55
62
49
68
66
65
62
69
66
73
64
87
87
66
74
61
71
67
67
71
74
65
58
65
54
66
62
55
59
49
61
48
66
95
106
102
100
94
100
104
90
69
73
57
61
53
42
50
41
60
46
39
41
41
58
63
60
63
68
70
71
69
62
63
61
59
72
82
68
83
63
63
64
66
39
76
60
60
63
66
65
62
65
71
66
67
77
61
43
51
49
51
51
49
60
61
50
65
62
78
78
71
77
73
75
72
72
76
81
63
61
71
39
58
65
47
47
48
63
49
64
69
65
68
67
61
71
75
72
66
73
65
76
91
66
86
65
86
80
80
82
84
66
70
70
62
81
60
71
72
72
70
80
Appendix 87
Ind.
3/1
3/2
3/3
3/
1
3/S
(
67
84
77
71
70
80
82
66
67
68
79
78
68
95
95
00
92
91
99
98
61
71
69
70
75
75
66
71
65
77
73
71
62
70
76
71
58
51
38
51
60
62
52
58
44
72
67
55
69
75
70
71
70
64
67
75
73
66
65
60
75
71
81
67
60
62
68
74
76
72
49
58
58
62
58
55
61
71
75
87
79
81
97
83
105
73
82
53
84
76
93
95
78
92
100
91
102
91
86
80
77
78
84
71
82
68
76
71
76
75
85
78
53
55
51
55
52
58
48
49
55
56
79
69
57
42
51
50
51
47
49
58
61
80
84
78
79
84
71
68
73
76
80
82
81
97
104
97
93
95
88
100
86
84
98
82
73
72
68
71
63
61
64
73
68
78
83
57
66
79
79
64
79
79
88
81
66
60
50
60
46
56
49
46
63
80
85
72
67
61
57
62
60
61
56
57
55
86
68
63
62
69
57
73
64
53
73
80
87
58
64
40
50
59
60
69
60
66
71
88
61
54
49
59
60
60
52
55
60
65
89
go
84
97
59
74
58
83
72
61
64
81
91
74
75
63
67
63
62
72
70
74
74
92
84
95
90
86
83
99
84
84
84
81
93
82
76
65
76
55
74
77
82
76
73
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